Chapter 4.6, Problem 12PPS

To determine

To find: the number of miles of the return trip

Answer to Problem 12PPS

The return trip was 536 miles.

Explanation of Solution

Given:

The total distance covered is 1356 miles.

The return trip is 284 miles shorter than the first part.

Calculation:

Let m be the number of miles on the first part of the trip.

The total distance covered is 1356 miles.

The return trip is 284 miles shorter than the first part.

So, the number of miles for the return trip is $m-284$ .

Putting all together, the required equation is,

  $m+m-284=1356\mathrm{........}\text{(1)}$

Solve the equation (1) for m

  $\begin{array}{l}m+m-284=1356\\ 2m-284=1356Distributive\mathrm{Pr}operty\\ 2m-284+284=1356+284Add284onbothsides\\ 2m=1640\\ \frac{2m}{2}=\frac{1640}{2}Divideby2onbothsides\\ m=820\end{array}$

Therefore, the first part of the trip covered a total distance of 820 miles.

Find the distance covered in the return trip.

  $\begin{array}{l}m-284=820-284\\ =536\end{array}$

Hence, the return trip was 536 miles.

Conclusion:

Hence, the return trip was 536 miles.