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Math Problems
Algebra 1
Rate of travel: word problems
Rosa's and Kiara's houses are separated by a stretch of road that is
24
24
24
miles long. One day, they decide to meet up somewhere in the middle and spend the afternoon together. Rosa leaves her house and travels at
48
48
48
miles per hour at the same time that Kiara leaves her house and drives
46
46
46
miles per hour. How long will it be until they meet?
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Nicholas walked to his friend Alan's house at a steady speed of
300
300
300
feet per minute. If the two friends live
2
,
400
2,400
2
,
400
feet apart, how long did it take Nicholas to walk to Alan's house? Write your answer as a whole number or decimal.
\newline
____ minutes
\newline
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Simon and his track team ran on the Heron Peak running trail yesterday after school. The team ran
2
2
2
miles due west from the parking lot to a bench. They turned at the bench to run
1.5
1.5
1.5
miles due north toward an outhouse. To finish the run, the team ran a straight line from the outhouse back to the parking lot. If Simon ran at a constant rate of
8
8
8
miles per hour, how long did it take Simon to finish the run?
\newline
If necessary, round your answer to the nearest tenth.
\newline
____ minutes
\newline
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A whale is swimming due north at a speed of
30
30
30
miles per hour. Just
5
5
5
miles away, a whale-watching tour boat is traveling south, directly toward the whale, at a speed of
46
46
46
miles per hour. How long will it be before they meet? If necessary, round your answer to the nearest minute.
_
_
\_\_
__
hours and
_
_
\_\_
__
minutes
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At a certain instant, the car is
9
9
9
meters from the intersection.
\newline
What is the rate of change of the distance between the car and the person at that instant (in meters per second)?
\newline
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A person stands
15
15
15
meters east of an intersection and watches a car driving towards the intersection from the north at
1
1
1
meter per second.
\newline
At a certain instant, the car is
8
8
8
meters from the intersection.
\newline
What is the rate of change of the distance between the car and the person at that instant (in meters per second)?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
65
-\sqrt{65}
−
65
\newline
(B)
−
2
-2
−
2
.
125
125
125
\newline
(C)
−
8
17
-\frac{8}{17}
−
17
8
\newline
(D)
−
17
-17
−
17
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A person stands
10
10
10
meters east of an intersection and watches a car driving towards the intersection from the north at
13
13
13
meters per second.
\newline
At a certain instant, the car is
24
24
24
meters from the intersection.
\newline
What is the rate of change of the distance between the car and the person at that instant (in meters per second)?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
26
-26
−
26
\newline
(B)
−
269
-\sqrt{269}
−
269
\newline
(C)
−
12
-12
−
12
\newline
(D)
−
169
12
-\frac{169}{12}
−
12
169
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A person stands
15
15
15
meters east of an intersection and watches a car driving towards the intersection from the north at
1
1
1
meter per second.
\newline
At a certain instant, the car is
8
8
8
meters from the intersection.
\newline
What is the rate of change of the distance between the car and the person at that instant (in meters per second)?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
65
-\sqrt{65}
−
65
\newline
(B)
−
8
17
-\frac{8}{17}
−
17
8
\newline
(C)
−
2
-2
−
2
.
125
125
125
\newline
(D)
−
17
-17
−
17
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A person stands
10
10
10
meters east of an intersection and watches a car driving towards the intersection from the north at
13
13
13
meters per second.
\newline
At a certain instant, the car is
24
24
24
meters from the intersection.
\newline
What is the rate of change of the distance between the car and the person at that instant (in meters per second)?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
269
-\sqrt{269}
−
269
\newline
(B)
−
26
-26
−
26
\newline
(C)
−
12
-12
−
12
\newline
(D)
−
169
12
-\frac{169}{12}
−
12
169
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The base of a triangle is increasing in length at a rate of
3
c
m
3 \mathrm{~cm}
3
cm
per second, while its height is decreasing at a rate of
2
c
m
2 \mathrm{~cm}
2
cm
per second. At the moment when the area of the triangle is
60
c
m
2
60 \mathrm{~cm}^{2}
60
cm
2
, its base is
20
c
m
20 \mathrm{~cm}
20
cm
long. Determine the rate of change of the area at this time.
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Two trains, each
400
400
400
meters long, pass each other completely in
10
10
10
seconds when they are moving in opposite directions. Moving in the same direction, they pass each other completely in
20
20
20
seconds.
\newline
Find the speed of the faster train.
\newline
40
40
40
meters per second
\newline
50
50
50
meters per second
\newline
60
60
60
meters per second
\newline
30
30
30
meters per second
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A herd of elephants on the savannah is moving in a straight line at
4
4
4
kilometers per hour, headed directly toward a biologist who has been tracking them. Meanwhile, the biologist is also driving toward them at
69
69
69
kilometers per hour. If they started out
14
14
14
kilometers apart, how long will it be before they encounter one another?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
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Some sailors are traveling due west in a lifeboat moving
5
5
5
kilometers per hour. A rescue boat is coming due east toward them at
29
29
29
kilometers per hour. If the boats are currently
49
49
49
kilometers apart, how long will it be before they meet?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
\newline
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Hakim and Frank just finished a picnic at the park and are about to ride their bikes home. Hakim goes
14
14
14
miles per hour, and Frank goes
11
11
11
miles per hour in precisely the opposite direction. In how long will they be
6
6
6
miles apart? If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
\newline
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Two freight trains leave the station in Lexington at the same time. The first train is headed due south at a speed of
22
22
22
miles per hour. In comparison, the second train is going due north at
35
35
35
miles per hour. In how long will the trains be
380
380
380
miles apart?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
\newline
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A twig floats downstream at a rate of
4
4
4
kilometers per hour. At the same time,
2
2
2
kilometers downstream, a trout begins swimming upstream, moving toward the twig at
16
16
16
kilometers per hour. In how much time will the fish swim by the twig?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
\newline
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Mrs. Brady's class takes a ferry east across a lake at
24
24
24
miles per hour. At the same time, a fishing boat leaves from the opposite side of the lake, traveling west at
52
52
52
miles per hour. The two vessels started out
1
1
1
mile apart and are now traveling directly toward each other. How long will it be before they pass by each other?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
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Mrs. Richmond's class is on a ferry that is traveling
41
41
41
kilometers per hour. The students notice that they are passing right by a fishing boat that is traveling in exactly the opposite direction at
89
89
89
kilometers per hour. How long will it be before the two vessels are
6
6
6
kilometers apart?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
\newline
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Brett took the train due south from the airport, heading to the end of the line. At the same time, Maddie also left home and started driving due north to the end of the line, where she would pick Brett up. Brett's train traveled
66
66
66
kilometers per hour, and Maddie drove
82
82
82
kilometers per hour. They started out
44
44
44
kilometers apart and arrived at the station at the same time. How long did it take them to meet?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
\newline
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An iceberg and a ship separated by
98
98
98
miles are moving directly toward each other. The iceberg is floating at
1
1
1
mile per hour, whereas the ship is traveling at
12
12
12
miles per hour. Assuming that neither changes course, how long will it be before the two collide?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
\newline
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Zane and Camilla are coworkers who live in different cities. They both left the office at the same time today. Camilla drove directly east toward Oxford at a speed of
37
37
37
miles per hour. Zane took the bus directly west toward Westminster, traveling
32
32
32
miles per hour. In how long were the two of them
44
44
44
miles apart?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
\newline
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Two groups of tourists are on the same floor of a skyscraper they are visiting, and they board adjacent elevators at the same time. The first group is headed up at a speed of
140
140
140
meters per minute. The second is headed down at a speed of
290
290
290
meters per minute. How long will it be before the elevators are
360
360
360
meters apart? If necessary, round your answer to the nearest second.
\newline
____ minutes and ____ seconds
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Valentina boards an elevator in the lobby that is headed up at
610
610
610
feet per minute. Meanwhile,
1
,
500
1,500
1
,
500
feet above, Owen boards an adjacent elevator headed down at
620
620
620
feet per minute. How long will it be before Valentina and Owen pass each other?
\newline
If necessary, round your answer to the nearest second.
\newline
____ minutes and ____ seconds
\newline
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After spending the winter in Fulton County, two flocks of birds are now migrating home. The first flock flies due east at
33
33
33
kilometers per hour, and the second flies west at
63
63
63
kilometers per hour. In how much time will they be
390
390
390
kilometers apart? If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
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A disabled sailboat is drifting on a current that is moving at
15
15
15
kilometers per hour. Fortunately, it's drifting toward a Coast Guard station
75
75
75
kilometers away, which picks up the distress call and sends a rescue craft directly toward the sailboat. The rescue craft can travel
53
53
53
kilometers per hour. How long will it be before the two vessels meet?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
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Jessica and Myra just met up in Cedarburg for the afternoon, and now it is time for them to get in their cars and head home. Jessica heads due east at
76
76
76
kilometers per hour, and Myra heads due west at
87
87
87
kilometers per hour. How long will it be until they are
63
63
63
kilometers apart?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
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Two buses depart from the Yardley Bus Terminal. One is moving north at
41
41
41
kilometers per hour, while the other is moving south at
27
27
27
kilometers per hour. How long will it be before the buses are
65
65
65
kilometers apart?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
\newline
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Helen and Reid are walking to their classes at Cedarburg College. Helen comes from her dorm room, walking at a speed of
4
4
4
miles per hour down a straight path. Reid comes from the gymnasium on the other end of campus, moving up the same path at
3
3
3
miles per hour. If they start out
3
3
3
miles apart, how long will it be before they meet?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
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The front of a brush fire is moving through some dead grass at a rate of
3
3
3
miles per hour. Luckily, it is moving directly toward the fire station, which can dispatch a fire truck to fight the blaze. If the fire station is
1
1
1
mile away and the truck can travel straight to the fire's front at
44
44
44
miles per hour, how long will it be before the fire truck reaches the fire's front? If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
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Two elevators open their doors at the same time. Kathleen boards the first one, which is going up at
800
800
800
feet per minute. The person next to her, Dominic, boards the second one, which is going down at
840
840
840
feet per minute. In how long will Kathleen and Dominic be
1
,
300
1,300
1
,
300
feet apart?
\newline
If necessary, round your answer to the nearest second.
\newline
____ minutes and ____ seconds
\newline
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Hugo lives in the northwest corner of Greene County, Lena lives
29
29
29
miles away in the southeast corner, and the office where they work is directly between them. On Monday, Hugo took the bus into work, taking a direct route at
32
32
32
miles per hour. Lena left at the same time, taking her car along a direct route at a speed of
36
36
36
miles per hour. The two coworkers arrive at the office at the same time. How long did the commute take? If necessary, round your answer to the nearest minute.
\newline
_
_
_
\_\_\_
___
hours and
_
_
_
\_\_\_
___
minutes
\newline
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Two flocks of birds are
210
210
210
miles apart and heading directly toward each other. One flock is flying at a rate of
25
25
25
miles per hour. In comparison, the other flock is flying at a rate of
37
37
37
miles per hour. In how much time will the two flocks meet?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
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Two groups of tourists are on the same floor of a skyscraper they are visiting, and they board adjacent elevators at the same time. The first group is headed up at a speed of
210
210
210
feet per minute. The second is headed down at a speed of
740
740
740
feet per minute. How long will it be before the elevators are
1
,
100
1,100
1
,
100
feet apart? If necessary, round your answer to the nearest second.
\newline
____ minutes and ____ seconds
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A plane leaves the Newberry airport, traveling due north at a rate of
900
900
900
kilometers per hour. At the same time, another plane departs from the same airport and travels due south at a rate of
1
,
200
1,200
1
,
200
kilometers per hour. In how long will the planes be
600
600
600
kilometers apart?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
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A freight train on the Bluepoint-Vindale line departs Bluepoint, traveling at a speed of
42
42
42
kilometers per hour. At the same time, a second train leaves Vindale, bound for Bluepoint, and is moving at
97
97
97
kilometers per hour. If the train line is
130
130
130
kilometers long, how much time will pass before the two trains meet?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
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A Coast Guard rescue craft just picked up the captain of a disabled sailboat. The rescue craft is now heading back to shore at a rate of
48
48
48
miles per hour. Meanwhile, the sailboat is drifting in the other direction at
3
3
3
miles per hour. How long will it be before the rescue craft is
41
41
41
miles from the sailboat?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
\newline
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Two groups of friends are taking taxis to a party in Yardley. The first taxi leaves from the financial district and travels at
33
33
33
miles per hour. At the same time, the other taxi leaves from the marina and travels
45
45
45
miles per hour. The two taxis are
5
5
5
miles apart and heading directly toward each other. How much time will it take for the taxis meet?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
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A van full of storm chasers is driving along a straight road at
94
94
94
kilometers per hour in hopes of filming a tornado. The tornado,
7
7
7
kilometers away, is traveling along the same road and moving directly toward them, traveling at
69
69
69
kilometers per hour. If neither the van nor the tornado changes course, how long will it be before they meet?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
\newline
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A ranch hand herded his cattle to some grazing land. Then he began riding back to the ranch, which is due west, at
3
3
3
miles per hour. Simultaneously, the cows began moving away from him, too, headed due east at
1
1
1
mile per hour. How long did it take for the herd and the ranch hand to be
3
3
3
miles apart? If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
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Two friends are windsurfing at a popular beach. Shawna is paddling out on her board, going
3
3
3
miles per hour. At the same time,
2
2
2
miles directly in front of Shawna, Peter has caught a big wave and is riding it back in at a rate of
15
15
15
miles per hour. In how much time will the two surfers pass each other?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
\newline
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Charlotte and Tyrone are hiking in a state park. They start at opposite ends of a trail that is
4
4
4
miles long and hike toward each other. Charlotte is moving at a speed of
3
3
3
miles per hour, whereas Tyrone is moving at a speed of
5
5
5
miles per hour. How much time will go by before they meet up? If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
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Barbara is kayaking on a river in Clinton County, moving down the river at a speed of
8
8
8
miles per hour. Meanwhile, Levi is on a jet ski
5
5
5
miles away, moving up the river at
27
27
27
miles per hour. How long will it be before the two meet?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
\newline
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Darnell and Roxanne just finished a picnic at the park and are about to ride their bikes home. Darnell goes
6
6
6
miles per hour, and Roxanne goes
7
7
7
miles per hour in precisely the opposite direction. In how long will they be
10
10
10
miles apart?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
\newline
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A large ice floe is floating toward a polar bear
7
7
7
kilometers away at a speed of
2
2
2
kilometers per hour. At the same time, the polar bear is swimming toward the ice floe at
5
5
5
kilometers per hour. How long will it be before the polar bear reaches the ice floe? If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
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A rescue boat just picked up some sailors in a lifeboat. Now the rescue boat is heading north at
14
14
14
miles per hour. The lifeboat, which they abandoned, is drifting south at a speed of
3
3
3
miles per hour. How long will it be before the rescued sailors are
57
57
57
miles from their lifeboat?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
\newline
Get tutor help
Rosa's and Kiara's houses are separated by a stretch of road that is
24
24
24
miles long. One day, they decide to meet up somewhere in the middle and spend the afternoon together. Rosa leaves her house and travels at
48
48
48
miles per hour at the same time that Kiara leaves her house and drives
46
46
46
miles per hour. How long will it be until they meet?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
\newline
Get tutor help
Helen and Elizabeth just met up in Springdale for the afternoon, and now it is time for them to get in their cars and head home. Helen heads due east at
95
95
95
kilometers per hour, and Elizabeth heads due west at
89
89
89
kilometers per hour. How long will it be until they are
77
77
77
kilometers apart?
\newline
If necessary, round your answer to the nearest minute.
\newline
_
_
_
\_\_\_
___
hours and
_
_
_
\_\_\_
___
minutes
\newline
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Two friends, Zeke and Marshall, are going to depart from their houses and ride their bikes toward each other until they meet, and then have a picnic. Zeke can bike
15
kilometers per hour
15 \, \text{kilometers per hour}
15
kilometers per hour
, while Marshall can bike
17
kilometers per hour
17 \, \text{kilometers per hour}
17
kilometers per hour
. If their houses are connected by a straight road that is
8
kilometers
8 \, \text{kilometers}
8
kilometers
long, in how long will the two meet? If necessary, round your answer to the nearest minute.
\newline
_
_
_
_
\_\_\_\_
____
hours and
_
_
_
_
\_\_\_\_
____
minutes
\newline
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A large ice floe is floating at a speed of
4
4
4
kilometers per hour. A polar bear leaves the floe and swims in the opposite direction at
7
7
7
kilometers per hour. How long will it be before the polar bear is
1
1
1
kilometer away from the floe? If necessary, round your answer to the nearest minute.
\newline
_
_
_
_
\_\_\_\_
____
hours and
_
_
_
_
\_\_\_\_
____
minutes
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Two freight trains leave the station in Allenville at the same time. The first train is headed due south at a speed of
43
43
43
kilometers per hour. In comparison, the second train is going due north at
64
64
64
kilometers per hour. In how long will the trains be
450
450
450
kilometers apart?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
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