Chapter 4.5, Problem 38PPS

To determine

To find: The number of hours the bus was on highway and for how long hours it was driving in the city.

Answer to Problem 38PPS

The number of hours the bus was on highway is 5hoursand in the city is 2hours.

Explanation of Solution

Given,

The set of equation is given as,

  $\begin{array}{l}65x+25y=375\\ x+y=7\end{array}$

Calculation:

Calculate the value of x .

  $\begin{array}{c}x=\frac{\left|\begin{array}{cc}375& 25\\ 7& 1\end{array}\right|}{\left|\begin{array}{cc}65& 25\\ 7& 1\end{array}\right|}\\ =\frac{375\left(1\right)-25\left(7\right)}{65\left(1\right)-25\left(1\right)}\\ =\frac{200}{40}\\ =5\end{array}$

Calculate the value of y .

  $\begin{array}{c}y=\frac{\left|\begin{array}{cc}65& 375\\ 7& 1\end{array}\right|}{\left|\begin{array}{cc}65& 25\\ 7& 1\end{array}\right|}\\ =\frac{65\left(7\right)-375\left(1\right)}{65\left(1\right)-25\left(1\right)}\\ =\frac{80}{40}\\ =2\end{array}$

Thus, the number of hours the bus was on highway is 5 hours and in the city is 2 hours.