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Math Problems
Grade 7
Calculate unit rates with fractions
Last summer, Kira traveled by boat to an island located
36
36
36
miles off the coast. If the boat reached the island after
3
3
3
hours, what was its speed?
\newline
Write your answer as a whole number or decimal.
\newline
____ miles per hour
\newline
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Desert tortoises are some of the slowest animals on Earth. A biologist observed a desert tortoise walk a distance of
90
90
90
feet in
5
5
5
minutes. What was its speed?
\newline
Write your answer as a whole number or decimal.
\newline
_
_
_
_
\_\_\_\_
____
feet per minute
\newline
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The Golden Gate Bridge in San Francisco is
8
,
981
8,981
8
,
981
feet long. A cyclist travels across the entire length of the bridge in
7
7
7
minutes. What is her speed?
\newline
Write your answer as a whole number or decimal.
\newline
____ feet per minute
\newline
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At a track meet, Pete ran in the
200
200
200
-meter dash and finished in
25
25
25
seconds. What was his speed? Write your answer as a whole number or decimal.
\newline
\newline
____ meters per second
\newline
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Trent's school is
1
,
320
1,320
1
,
320
feet from his house. If he walks that distance in
5
5
5
minutes, what is his speed? Write your answer as a whole number or decimal.
\newline
____ feet per minute
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Shelley's cup of tea cooled down
1
2
\frac{1}{2}
2
1
of a degree in
10
10
10
seconds. At what rate is her tea cooling down?
\newline
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
\newline
____ degrees per second
\newline
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The copy machine at the library made a copy of Leslie's
3
3
3
-page essay in just
1
10
\frac{1}{10}
10
1
of a minute. What is the speed of the copy machine?
\newline
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
\newline
____ pages per minute
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Jen rode her bike
1
5
\frac{1}{5}
5
1
of a mile to her friend's house. It took her
5
5
5
minutes to get there. What was Jen's speed?
\newline
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
\newline
____ miles per minute
\newline
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A school janitor has mopped
1
3
\frac{1}{3}
3
1
of a classroom in
5
5
5
minutes. At what rate is he mopping?
\newline
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
\newline
____ classrooms per minute
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The Doyle family uses up a
1
2
\frac{1}{2}
2
1
-gallon jug of milk every
3
3
3
days. At what rate do they drink milk?
\newline
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
\newline
_
_
\_\_
__
gallons per day
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With some species of bamboo, you can actually see them grow. You could observe
30
30
30
centimeters of growth in just
1
/
3
1/3
1/3
of a day. At what rate does this bamboo grow?
\newline
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
\newline
_
_
_
\_\_\_
___
centimeters per day
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An airplane cruises
1
1
1
kilometer in
1
12
\frac{1}{12}
12
1
of a minute. What is its cruising speed?
\newline
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
\newline
____ kilometers per minute
\newline
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The Atlas V Rocket could go
1
1
1
full mile in just
1
10
\frac{1}{10}
10
1
of a second. How fast did it travel?
\newline
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
\newline
____ miles per second
\newline
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Shelley's cup of tea cooled down
1
2
\frac{1}{2}
2
1
of a degree in
10
10
10
seconds. At what rate is her tea cooling down?
\newline
Simplify your answer and write it as a proper fraction, mixed number, or whole number. _______degrees per second
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A young sumo wrestler decided to go on a special diet to gain weight rapidly.
\newline
W
W
W
represents the wrestler's weight (in kilograms) as a function of time
t
t
t
(in months).
\newline
W
=
80
+
5.4
t
W=80+5.4t
W
=
80
+
5.4
t
\newline
How much weight does the wrestler gain every
2
2
2
months?
\newline
□
\square
□
kilograms
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A
5
5
5
-meter ladder is sliding down a vertical wall so the distance between the bottom of the ladder and the wall is increasing at
6
6
6
meters per minute.
\newline
At a certain instant, the top of the ladder is
3
3
3
meters from the ground.
\newline
What is the rate of change of the area formed by the ladder at that instant (in square meters per minute)?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
7
-7
−
7
\newline
(B)
6
6
6
\newline
(C)
18
18
18
\newline
(D)
−
14
-14
−
14
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A
25
25
25
-meter ladder is sliding down a vertical wall so the distance between the bottom of the ladder and the wall is increasing at
3
3
3
.
5
5
5
meters per minute.
\newline
At a certain instant, the top of the ladder is
7
7
7
meters from the ground.
\newline
What is the rate of change of the distance between the top of the ladder and the ground at that instant (in meters per minute)?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
12
-12
−
12
\newline
(B)
−
7
-7
−
7
\newline
(C)
−
24
-24
−
24
\newline
(D)
−
3
-3
−
3
.
5
5
5
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A person stands
30
30
30
meters east of an intersection and watches a car driving away from the intersection to the north at
17
17
17
meters per second.
\newline
At a certain instant, the car is
16
16
16
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)
34
34
34
\newline
(B)
8
8
8
\newline
(C)
36
36
36
.
125
125
125
\newline
(D)
1189
\sqrt{1189}
1189
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The side of a cube is increasing at a rate of
2
2
2
kilometers per hour.
\newline
At a certain instant, the side is
1
1
1
.
5
5
5
kilometers.
\newline
What is the rate of change of the volume of the cube at that instant (in cubic kilometers per hour)?
\newline
Choose
1
1
1
answer:
\newline
(A)
13.5
\mathbf{1 3 . 5}
13.5
\newline
(B)
16.5
\mathbf{1 6 . 5}
16.5
\newline
(C)
8
8
8
\newline
(D)
2
2
2
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The side of a cube is decreasing at a rate of
9
9
9
millimeters per minute.
\newline
At a certain instant, the side is
19
19
19
millimeters.
\newline
What is the rate of change of the volume of the cube at that instant (in cubic millimeters per minute)?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
3249
-3249
−
3249
\newline
(B)
−
6859
-6859
−
6859
\newline
(C)
−
9747
-9747
−
9747
\newline
(D)
−
729
-729
−
729
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A
5
5
5
-meter ladder is sliding down a vertical wall so the distance between the bottom of the ladder and the wall is increasing at
6
6
6
meters per minute.
\newline
At a certain instant, the top of the ladder is
3
3
3
meters from the ground.
\newline
What is the rate of change of the area formed by the ladder at that instant (in square meters per minute)?
\newline
Choose
1
1
1
answer:
\newline
(A)
6
6
6
\newline
(B)
−
14
-14
−
14
\newline
(C)
18
\mathbf{1 8}
18
\newline
(D)
−
7
-7
−
7
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The base of a triangle is decreasing at a rate of
13
13
13
millimeters per minute and the height of the triangle is increasing at a rate of
6
6
6
millimeters per minute.
\newline
At a certain instant, the base is
5
5
5
millimeters and the height is
1
1
1
millimeter.
\newline
What is the rate of change of the area of the triangle at that instant (in square millimeters per minute)?
\newline
Choose
1
1
1
answer:
\newline
(A)
21
21
21
.
5
5
5
\newline
(B)
−
8
-8
−
8
.
5
5
5
\newline
(C)
−
21
-21
−
21
.
5
5
5
\newline
(D)
8
8
8
.
5
5
5
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A
39
39
39
-meter ladder is sliding down a vertical wall so the distance between the bottom of the ladder and the wall is increasing at
10
10
10
meters per minute.
\newline
At a certain instant, the bottom of the ladder is
36
\mathbf{3 6}
36
meters from the wall.
\newline
What is the rate of change of the distance between the top of the ladder and the ground at that instant (in meters per minute)?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
12
-12
−
12
\newline
(B)
−
25
6
-\frac{25}{6}
−
6
25
\newline
(C)
−
24
-24
−
24
\newline
(D)
−
10
-10
−
10
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The side of a cube is increasing at a rate of
2
2
2
kilometers per hour.
\newline
At a certain instant, the side is
1
1
1
.
5
5
5
kilometers.
\newline
What is the rate of change of the volume of the cube at that instant (in cubic kilometers per hour)?
\newline
Choose
1
1
1
answer:
\newline
(A)
2
2
2
\newline
(B)
16.5
\mathbf{1 6 . 5}
16.5
\newline
(C)
8
8
8
\newline
(D)
13.5
\mathbf{1 3 . 5}
13.5
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The side length of a square is decreasing at a rate of
2
2
2
kilometers per hour.
\newline
At a certain instant, the side length is
9
9
9
kilometers.
\newline
What is the rate of change of the area of the square at that instant (in square kilometers per hour)?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
324
-324
−
324
\newline
(B)
−
4
-4
−
4
\newline
(C)
−
36
-36
−
36
\newline
(D)
−
81
-81
−
81
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The side length of a square is increasing at a rate of
15
15
15
millimeters per second.
\newline
At a certain instant, the side length is
22
22
22
millimeters.
\newline
What is the rate of change of the area of the square at that instant (in square millimeters per second)?
\newline
Choose
1
1
1
answer:
\newline
(A)
225
225
225
\newline
(B)
660
660
660
\newline
(C)
484
484
484
\newline
(D)
30
30
30
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A
10
10
10
-meter ladder is sliding down a vertical wall so the distance between the top of the ladder and the ground is decreasing at
3
3
3
meters per minute.
\newline
At a certain instant, the bottom of the ladder is
6
6
6
meters from the wall.
\newline
What is the rate of change of the area formed by the ladder at that instant (in square meters per minute)?
\newline
Choose
1
1
1
answer:
\newline
(A)
12
12
12
\newline
(B)
−
7
2
-\frac{7}{2}
−
2
7
\newline
(C)
7
7
7
\newline
(D)
−
6
-6
−
6
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The side of a cube is decreasing at a rate of
9
9
9
millimeters per minute.
\newline
At a certain instant, the side is
19
19
19
millimeters.
\newline
What is the rate of change of the volume of the cube at that instant (in cubic millimeters per minute)?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
729
-729
−
729
\newline
(B)
−
9747
-9747
−
9747
\newline
(C)
−
6859
-6859
−
6859
\newline
(D)
−
3249
-3249
−
3249
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A man travels from Town
A
A
A
to Town
B
B
B
at an average speed of
4
k
m
/
h
4 \mathrm{~km} / \mathrm{h}
4
km
/
h
and from Town B to Town A at an average speed of
6
k
m
/
h
6 \mathrm{~km} / \mathrm{h}
6
km
/
h
. If he takes
45
45
45
minutes to complete the entire journey, find
h
is
h_{\text {is }}
h
is
total distance travelled.
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In
2009
2009
2009
, Usain Bolt set the world record for sprinting
100
m
100\,\text{m}
100
m
in approximately
9.58
9.58
9.58
seconds. Find his average speed in meters per second.
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Shandra read
1
1
1
book in
5
5
5
months. What was her rate of reading, in books per month? Give your answer as a whole number or a FRACTION in simplest form.
\newline
Answer:
□
\square
□
books per month
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Fwam read
10
10
10
books in
5
5
5
months. What was his rate of reading, in books per month? Give your answer as a whole number or a FRACTION in simplest form.
\newline
Answer:
□
\square
□
books per month
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Kaylee read
12
12
12
books in
4
4
4
months. What was her rate of reading, in books per month? Give your answer as a whole number or a FRACTION in simplest form.
\newline
Answer:
□
\square
□
books per month
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The side of the base of a square prism is decreasing at a rate of
−
7
-7
−
7
kilometers per minute and the height of the prism is increasing at a rate of
10
10
10
kilometers per minute.
\newline
At a certain instant, the base's side is
4
4
4
kilometers and the height is
9
9
9
kilometers.
\newline
What is the rate of change of the surface area of the prism at that instant (in square kilometers per minute)?
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Maddy is carrying a
5
liter
5\,\text{liter}
5
liter
jug of sports drink that weighs
7.5
kg
7.5\,\text{kg}
7.5
kg
. She wants to know how many kilograms a
2
liter
2\,\text{liter}
2
liter
jug of sports drink would weigh
(
w
)
(w)
(
w
)
. She assumes the relationship between volume and weight is proportional. What is the weight of the
2
liter
2\,\text{liter}
2
liter
jug?
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Mr. Sonny's science class is calculating the average number of blinks per minute. Jan blinks
303
303
303
times in
3
3
3
minutes. What is her blinking rate, in blinks per minute?
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Claire is a teacher and takes home
90
90
90
papers to grade over the weekend. She can grade at a rate of
11
11
11
papers per hour. How many papers would Claire have remaining to grade after working for
5
5
5
hours?
\newline
Answer:
□
\square
□
papers
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P
=
47.4
(
G
−
174.5
)
P = 47.4(G - 174.5)
P
=
47.4
(
G
−
174.5
)
The profit,
P
P
P
, in dollars, to an amusement park serving
G
G
G
guests over one day is given by the equation. What is the minimum number of guests that need to be served in order to make a positive profit?
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Harvey the wonder hamster can run
3
1
6
k
m
3 \frac{1}{6} \mathrm{~km}
3
6
1
km
in
1
4
\frac{1}{4}
4
1
hour. Harvey runs at a constant rate.
\newline
Find his average speed in kilometers per hour.
\newline
kilometers per hour
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In
2009
2009
2009
, Usain Bolt set the world record for sprinting
100
m
100 \mathrm{~m}
100
m
in approximately
9
3
5
9 \frac{3}{5}
9
5
3
seconds.
\newline
Find his average speed in meters per second.
\newline
meters per second
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The energy usages per day (in kilowatt-hours) of houses on Hamlet Avenue are listed below.
\newline
30
,
23
,
38
,
36
,
33
30,23,38,36,33
30
,
23
,
38
,
36
,
33
\newline
Find the mean energy usage per day.
\newline
k
W
h
\mathrm{kWh}
kWh
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To determine her resting heart rate, an athlete counts her pulse for
10
10
10
seconds. She counts
9
9
9
beats in
10
10
10
seconds. What is her resting heart rate in beats per minute (bpm)?
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