Question

Assume that the cheetah travels an average of 40 mph to go from its resting place to a rock near a river. On the return trip to its resting place, the cheetah travels an average of 70 mph. If the cheetah traveled for 15 minutes, how many minutes did the return trip take to the nearest minute and second?
a. Set up the table as follows. Label the rows "To the River" and "From the River." Label the
columns "Distance," "Rate," and "Time (in Hours). Let t represent the unknown quantity in the
problem. Fill in the table.
b. From the table, set up an equation relating the distances.
c. Solve the problem. Write the answer in a complete sentence, stating it in terms of minutes and
seconds

Answer 1

Answer:

The return trip take 5 minutes 27 seconds

Step-by-step explanation:

Let

x -----> the time it take the cheetah travels to go from its resting place to a rock near a river in hours

y ----> the time it take the cheetah the return trip to its resting place in hours

we know that

The distance from its resting place to a rock near a river is the same that the return trip

The average speed multiplied by the time is equal to distance

so

The total time is 15 minutes

Convert to hours

15 min=15/60 hours

x+y=(15/60)

x+y=1/4

4x+4y=1 -----> equation A

40x=70y ----> equation B

Solve the system by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

The solution is the point ( 0.1591,0.0909)

see the attached figure

The time it take the cheetah travels to go from its resting place to a rock near a river is 0.1591 hours

The time it take the cheetah the return trip to its resting place is 0.0909 hours

Convert to minutes and seconds

0.0909 hours=0.0909(60)=5.454 minutes

o.454 minutes=0.454(6)=27.24 seconds

therefore

The return trip take 5 minutes 27 seconds

To the river

The time it take the cheetah travels to go from its resting place to a rock near a river is 0.1591 hours

The rate is 40 mph

To find out the distance multiply the average rate by the time

Find out the distances

The distance from its resting place to a rock near a river is

$d_1=40x=40(0.1591)=6.36\ miles$

From the river

The time it take the cheetah the return trip to its resting place is 0.0909 hours

The rate is 70 mph

To find out the distance multiply the average rate by the time

Find out the distances

The distance of the return trip is

$d_2=70x=70(0.0909)=6.36\ miles$

Both distances are the same