SOLUTION: I'm a little stuck on how to go about setting up this problem, Thanks! A family has two cars. During one particular week, the first car consumed 40 gallons of gas and the secon

Question 969338: I'm a little stuck on how to go about setting up this problem, Thanks!
A family has two cars. During one particular week, the first car consumed 40
gallons of gas and the second consumed 25 gallons of gas. The two cars drove a combined total of 1425 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?
Found 2 solutions by Boreal, solver91311:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Car 1 gets x miles per gallon
Car 2 gets 45-x mpg, because the same of the two is 45. We have only one variable.
Miles driven by car 1 is 40 gallons * x mi/gallon=40x miles
Miles driven by car 2 is 25 gallons *(45-x) mi/gallon= 1125-25x miles
Miles driven by both are the sum, which is 40x +1125-25x. This is 1125 + 15x
But we know the miles driven were 1425.
Therefore, 1125+15x=1425. Subtracting 1125 from each side, we get
15x=300
x=20 (300/15) mpg Car 1
45-x=25 mpg Car 2
So car 1 at 20 mpg *40 gallons drove 800 miles
car 2 at 25 mpg *25 gallons drove 625 miles
800 + 625 =1425 miles as a check.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The sum of the distances traveled by car 1 and car 2 was 1425 miles, so

Since the assignment of variable names is arbitrary we can assume without loss of generality that car 1 is the car that used 40 gallons of gas. So if is the distance traveled by that car, the fuel efficiency of that car is . Likewise the efficiency of the second car is . The sum of these two fuel efficencies is given as 45, hence:

Solve the 2X2 system of equations for and

John

My calculator said it, I believe it, that settles it

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