Chapter 6.5, Problem 31PFA

To determine

To calculate the distance that Terence drove.

Answer to Problem 31PFA

146 miles

Explanation of Solution

Given:

Terence drove 32 miles more than his father.

Together, they drove 260 miles.

Calculation:

Let x be the distance that Terence drove and y be the distance that Terence’s father drove.

Given that they drove 260 miles together,

  $\Rightarrow x+y=\mathrm{260................}(1)$

Also, Terence drove 32 miles more than his father.

  $\Rightarrow x=32+y\mathrm{.................}(2)$

Substitute (2) in (1)

  $\begin{array}{l}\Rightarrow (32+y)+y=260\\ \Rightarrow 32+2y=260\\ \Rightarrow 2y=260-32\\ \Rightarrow 2y=228\\ \Rightarrow y=114\end{array}$

Substitute $y=114$ in equation (2).

  $\begin{array}{l}\Rightarrow x=32+114\\ \Rightarrow x=146\end{array}$

Conclusion:

Therefore, Terence drove 146 miles.