Chapter 4.8, Problem 7P

To determine

To calculate: Time atAndrew and Stacey meet each other.

Answer to Problem 7P

11:30 am.

Explanation of Solution

Given information:

At 9:30 A.M. Andrew left Exeter for Portsmouth cycling at 12min/hr.

At 10 A.M. Stacey left Portsmouth for Exeter cycling at 16min/hr.

The distance from Exeter to Portsmouth is 20 miles.

Formula used: $distance=speed\times time$

Calculation:

According to question,

Let, t= Stacey’s travel time

  $\left(t+0.5\right)$ = Andrew’s travel time (started a half hour earlier than Stacey)

The distance equation is given by,

  $distance=speed\times time$

Stacey distance = $16t$

Andrew’s distance = $12(t+0.5)$

When Stacey overtakes Andrew, they have travelled the same distance,

Therefore,

  $Stacey’sdistance=Andrew’sdistance$

  $\begin{array}{l}16t=12\left(t+0.5\right)\\ 16t=12t+6\\ 16t-12t=6\\ 4t=6\\ t=\frac{6}{4}\\ t=1.5hrs=1:30hours\end{array}$

Stacey’s travel time started at 10:00A.M,

Thus,

  $10:00+1:30=11:30AM$ when Stacey overtakes Andrew.

Confirmingit by finding the actual distance each travelled,

  $\begin{array}{l}Andrew:12\left(1.5+.5\right)=24km\\ Stacey:16\left(1.5\right)=24km\end{array}$

Since both of them travelled same distance the equation formed is correct.

So, they met at 11:30 A.M.