Chapter 2, Problem 72A

To determine

Average speed for the second half of the trip.

To identify: Whether the obtained speed is reasonable or not.

Answer to Problem 72A

Average speed for the second half of the trip is 720 km/hr . It is not reasonable because it is not possible to attain this speed.

Explanation of Solution

Given:

Average speed of the trip is 90 km/hr and average speed for the first half of the trip is 48 km/hr.

Formula used:

Time taken to cover distance d with a speed of v is

  $t=\frac{d}{v}$

Calculation:

Let the total distance of the trip be dkm .

Half distance of the trip is $\frac{d}{2}\text{ km}$

Time taken to cover first half of the distance.

  $\begin{array}{c}t=\frac{\frac{d}{2}}{48}\\ =\frac{d}{96}\text{ hr}\end{array}$

Let velocity for the second half of the trip is v .

So, time taken to cover the second half of the distance.

  $\begin{array}{c}t=\frac{\frac{d}{2}}{v}\\ =\frac{d}{2v}\end{array}$

Average speed of the total trip is given as 90 km/hr. Total distance travelled isd km.

Therefore,

  $\begin{array}{l}v=\frac{d}{t}\\ 90=\frac{d}{\frac{d}{96}+\frac{d}{2v}}\\ 90=\frac{d}{d\left[\frac{1}{96}+\frac{1}{2v}\right]}\\ 90=\frac{1}{\frac{1}{96}+\frac{1}{2v}}\\ 90=\frac{1}{\frac{v+48}{96v}}\\ 90=\frac{96v}{v+48}\\ 90v+4320=96v\\ 6v=4320\\ v=720\text{ km/hr}\end{array}$

This speed is not reasonable because it is not possible to attain this speed.

Conclusion:

Therefore, speed for the second half of the strip is 720 km/hr. Since this speed is not possible to attain so it is not reasonable.