Question

An emergency vehicle travels 10 miles at a speed of 50 miles per hour. How fast must the vehicle travel on the return trip if the round-trip travel time is to be 20 minutes?

Answer 1

Step 1:

Given:

The distance covered by the vehicle $=10miles$

The speed of the vehicle $=50miles/hour$

Step 2:

Finding the time taken by the vehicle for the up journey:

We know that,

$$\begin{gathered} Time=\frac{Dis\tan ce}{Speed} \\ Bysubstitutingthegivenvalues,weget \\ =\frac{10}{50} \\ =\frac{1}{5}hours \\ =\frac{1}{5}\times 60min \\ =12min \end{gathered}$$

Finding the time remaining for the return journey:

$$\begin{gathered} Timetakenforreturnjourney=timeofroundjourney-timeofupjourney \\ =20min-12min \\ =8min \\ =8\times \frac{1}{60}hours \\ =\frac{2}{15}hours \end{gathered}$$

Finding the speed of the vehicle during the return journey:

We know that,

$$\begin{gathered} Speed=\frac{dis\tan ce}{time} \\ Bysubstitutingthegivenvaluesintheaboveexpression,weget \\ Speed=\frac{10}{\left({\displaystyle \frac{2}{15}}\right)}=\frac{150}{2}=75miles/hour \end{gathered}$$

Hence, the vehicle must travel at a speed of 75 miles/hour during the down journey to complete the trip in 20 mins.