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Math Problems
Algebra 1
Rate of travel: word problems
Two buses are scheduled to arrive at the Middletown Bus Terminal at the same time. One bus is south of the terminal, driving north at
26
26
26
miles per hour. At the same time, another bus is north of the terminal and is driving south at
59
59
59
miles per hour. They are currently
70
70
70
miles apart. How long will it be before the buses arrive at the terminal?
\newline
If necessary, round your answer to the nearest minute.
\newline
____ hours and ____ minutes
\newline
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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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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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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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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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A car travels at a speed of
60
km/h
60\,\text{km/h}
60
km/h
, while a bicycle travels at a speed of
20
km/h
20\,\text{km/h}
20
km/h
. If they both start at the same time and travel in the same direction, how long will it take for the car to be
30
kilometers
30\,\text{kilometers}
30
kilometers
ahead of the bicycle?
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A bicycle is travelling at
12
12
12
miles per hour. How many feet will it cover in
45
45
45
seconds?
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Given that events A and B are independent with
P
(
A
)
=
0.9
P(A)=0.9
P
(
A
)
=
0.9
and
P
(
B
)
=
0.3
P(B)=0.3
P
(
B
)
=
0.3
, determine the value of
P
(
A
∣
B
)
P(A \mid B)
P
(
A
∣
B
)
, rounding to the nearest thousandth, if necessary.
\newline
Answer:
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Given that events A and B are independent with
P
(
A
)
=
0.56
P(A)=0.56
P
(
A
)
=
0.56
and
P
(
B
)
=
0.35
P(B)=0.35
P
(
B
)
=
0.35
, determine the value of
P
(
A
∣
B
)
P(A \mid B)
P
(
A
∣
B
)
, rounding to the nearest thousandth, if necessary.
\newline
Answer:
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Rupert has a collection of Blu-ray discs he wants to store in a cubical box with edges of length
10
10
10
inches. If each Blu-ray has dimensions of
5
5
5
inches by
5
5
5
inches by
0.25
i
n
c
h
0.25 \mathrm{inch}
0.25
inch
, what is the maximum number of discs that can be fit into the box?
\newline
A)
60
60
60
\newline
B)
80
80
80
\newline
C)
160
160
160
\newline
D)
200
200
200
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A big cruise ship dropped anchor off the Caribbean island of Antigua. The heavy anchor dropped into the water at a rate of
2.5
meters per second
2.5\,\text{meters per second}
2.5
meters per second
. After
45
seconds
45\,\text{seconds}
45
seconds
, the anchor was
40
meters
40\,\text{meters}
40
meters
below the water's surface.
\newline
From what height
above the water’s surface
\text{above the water's surface}
above the water’s surface
was the anchor released?
\newline
□
\square
□
meters
\text{meters}
meters
\newline
How long did it take the anchor to reach the water's surface?
\newline
□
\square
□
seconds
\text{seconds}
seconds
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Two people are at an elevator. At the same time one person starts to walk away from the elevator at a rate of
2
ft/sec
2\,\text{ft/sec}
2
ft/sec
and the other person starts going up in the elevator at a rate of
7
ft/sec
7\,\text{ft/sec}
7
ft/sec
. What rate is the distance between the two people changing
15
15
15
seconds later?
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A
l
l
l
-meter ladder is sliding down a vertical wall so the distance between the top of the ladder and the ground is decreasing at
v
v
v
meters per minute. At a certain instant, the bottom of the ladder is
b
b
b
meters from the wall. What is the rate of change of the area formed by the ladder at that instant (in square meters per minute)?
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The top of a
25
25
25
foot ladder is sliding down a vertical wall at a constant rate of
4
4
4
feet per minute. When the top of the ladder is
15
15
15
feet off the ground, what is the rate of change of the distance between the bottom of the ladder and the wall?
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A controversial story comes out in the school newspaper. The number of students who have not heard about the story decreases at a rate that is proportional at any time to the number of students who have not heard the story at that time.
\newline
There were
900
900
900
students who had not heard the story initially, and the number of students is divided by
3
3
3
every
4
4
4
days.
\newline
How many students have not heard the story after
7
7
7
days?
\newline
Round to the nearest student.
\newline
□
\square
□
students
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George is driving at an average speed of
70
70
70
miles per hour. At this rate, how long, in minutes, will it take him to complete a
400
400
400
-mile road trip?
\newline
(Round your answer to the nearest minute.)
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Standard movie projectors project
24
24
24
still images, known as frames, each second. If a certain movie uses the standard frame rate and has exactly
129
129
129
,
600
600
600
total frames, then, to the nearest whole minute, how long is the movie?
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A wildfire is spreading toward a ranger station at a rate of
6
6
6
miles per hour. If the ranger station is
5
5
5
miles away from the wildfire, how many minutes will it take for the wildfire to reach the ranger station?
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An airplane begins its descent to land from a height of
35
35
35
,
000
000
000
feet above sea level. The airplane's height changes by about
−
4000
-4000
−
4000
feet every
3
3
3
minutes. Rounded to the nearest minute, in approximately how many minutes will the plane land? Assume that the airport runway is at sea level.
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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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