Question

A family has two cars. During one particular week, the first car consumed 20 gallons of gas and the second consumed 40 gallons of gas. The two cars drove a combined total of 1200 miles, and the sum of their fuel efficiencies was 45 miles per gallon. What were the fuel efficiencies of each of the cars that week? Note that the ALEKS graphing calculator can be used to make computations easier. First car: miles per gallon Second car: miles per gallon ?

Answer 1

Solution:

Let the car efficiency of first car be x

Let the car efficiency of the second car be y

Given that the first car consumed 20 gallons of gas and the second consumed 40 gallons of gas. The two cars drove a combined total of 1200 miles

This can be represented as

$20x+40y=1200-----(1)$

Given that the sum of their fuel efficiencies was 45 miles per gallon

This can be represented as

$x+y=45----------(11)$

Solve both equations simultaneously

$\begin{gathered} 20x+40y=1200 \\ x+y=45 \\ x=45-y \\ thus,\text{ } \\ 20(45-y)+40y=1200 \\ 900-20y+40y=1200 \\ 900+20y=1200 \\ 20y=1200-900 \\ y=\frac{300}{20} \\ y=15 \\ \end{gathered}$$\begin{gathered} x+y=45 \\ x=45-y \\ x=45-15 \\ x=30 \end{gathered}$

Thus,

First car: 30 miles per gallon

Second car: 15 miles per gallon