Chapter 4.8, Problem 19P

To determine

The time after which they meet

Answer to Problem 19P

The time after which they meet is $t=\frac{d}{r+s}$

Explanation of Solution

Given information:

Cars A and B travel the same road.

A's speed is $\text{rkm}/\text{h}$ and $\text{B's}$ speeds is $\text{s}\text{km}/\text{h}$ .

A and B travel towards each other at the same time.

Let they meet at $x\text{km}$ from A's end.

Then at this point distance covered by B will be $(d-x)\text{km}$ .

Then distance covered by A will be:

  $\text{Distance}=(\text{speed})(\text{time})$

  $x=rt$

Distance covered by B will be:

  $\begin{array}{l}d-x=st\\ d-rt=st\\ d=rt+st\\ d=t(r+s)\\ t=\frac{d}{r+s}\end{array}$

So, the time after which they meet is $t=\frac{d}{r+s}$