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

The road from the river takes nearly 5 minutes 27 seconds, the road to the river takes nearly 9 minutes 33 seconds

Explanation:

Use the formula
`D=r\cdot t,` where D is the distance, r is the rate and t is the time.

Note that 15 minutes
`=(15)/(60)=(1)/(4)=0.25` hour.

A. Set up the table as follows:

`\begin{array}{cccc}&\text{Rate}&\text{Time}&\text{Distance}\\ \\\text{To the River}&40\ mph&0.25-t&40(0.25-t)\\\text{From the River}&70\ mph&t&70t\end{array}`

B. The distance covered by cheetah is the same to the river and from the river, so

`40(0.25-t)=70t`

C. Solve this equation:

`40(0.25-t)=70t\\ \\10-40t=70t\\ \\110t=10\\ \\t=(10)/(110)=(1)/(11)\ hour`

Now

`(1)/(11)\ hour = (1)/(11)\cdot 60\ minutes=(60)/(11)\ minutes=5(5)/(11)\ minutes`

Thus, the road from the river takes nearly 5 minutes 27 seconds, the road to the river takes nearly 9 minutes 33 seconds.