Question

Please help A family has two cars. During one particular week, the first car consumed 40 gallons of gas and the second consumed 15 gallons of gas. The two cars drove acombined total of 1975 miles, and the sum of their fuel efficiencies was 65 miles per gallon. What were the fuel efficiencies of each of the cars that week?

Answer 1

Let's define the following variables.

x = fuel efficiency of Car 1

y = fuel efficiency of Car 2

Therefore, 40x + 15y = a total of 1975 miles.

Another given data is that the sum of the fuel efficiency of the two cars is 65 miles per gallon, therefore, x + y = 65.

We now have two equations:

1. 40x + 15y = 1975

2. x + y = 65

To solve for x and y, let's use the substitution method. Let's equation the second equation into y. So, equation 2 becomes y = 65 - x. Using this, we'll substitute the value of y in the first equation,

`\begin{gathered} 40x+15y=1975 \\ 40x+15(65-x)=1975 \\ 40x+975-15x=1975 \\ 40x-15x=1975-975 \\ 25x=1000 \\ (25x)/(25)=(1000)/(25) \\ x=40 \end{gathered}`

Therefore, the fuel efficiency of Car 1 is 40 miles per gallon.

Since we now have the value of x, let's solve for the value of y.

`\begin{gathered} y=65-x \\ y=65-40 \\ y=25 \end{gathered}`

Therefore, the fuel efficiency of Car 2 is 25 miles per gallon.