Chapter CSB1.3, Problem 22E

To determine

In how many seconds the two drivers will meet again at the starting point.

Answer to Problem 22E

Both drivers will meet again in $T=60\text{s}$

Explanation of Solution

Given:

One driver takes 30 seconds to complete 1-mile circular track.

Another driver takes 20 seconds to complete the same circular track.

Both drivers started at the same point.

As the track is circular and one driver takes 30 seconds to complete while other takes 20 seconds to complete the same track.

So, the time they will meet again will be the LCM of time taken by both drivers.

i.e.

  $\begin{array}{l}T=LCM\left(30,20\right)\\ \Rightarrow T=60\text{s}\end{array}$