Chapter 6.3, Problem 2P

To determine

To calculate: How long does it take to wash one car and one truck.

Answer to Problem 2P

20 minutes will be taken to wash one car and 30 minutes will be taken to wash one truck

Explanation of Solution

Given information: Let, x be the time (in minutes)taken by one car and y be the time (in minutes) taken by one truck.

2 cars and 3 trucks take 130 minutes i.e. $2x+3y=130$

2 cars and 5 trucks take 190 minutes i.e. $2x+5y=190$

Calculation:

Equation to be solved:

  $\begin{array}{l}2x+3y=130\mathrm{...}\left(i\right)\\ 2x+5y=190\mathrm{...}\left(ii\right)\end{array}$

Solve the equation using elimination method:

  $\begin{array}{l}2x+3y=130\\ 2x+5y=190\\ \underset{\_}{---}\\ 2x-2x+3y-5y=130-190\\ -2y=-60\\ y=\frac{-60}{-2}\\ \boxed{y=30\min }\end{array}$

Put the value of $y$ in equation ( i )

  $\begin{array}{l}2x+3\left(30\right)=130\\ 2x+90=130\\ 2x=130-90\\ 2x=40\\ \boxed{x=20\min }\end{array}$