A family has two cars. The first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of 40 miles per gallon of gas.

Question

A family has two cars. The first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of 40 miles per gallon of gas. During one particular week, the two cars went a combined total of 1850 miles, for a total gas consumption of 50 gallons. How many gallons were consumed by each of the two cars that week?

Answer 1

Let x = gallons consumed by car 1

Let y = gallons consumed by car 2

 

 

We set up our equations:

 

35x+40y = 1850        eq1

x+y = 50                   eq2

 

Substituting eq 2 into eq 1,

 

35x+40(50-x) = 1850

35x+2000-40x = 1850

-5x+2000 = 1850

-5x = -150

   x = 30

 

Substitute value of x into eq 2.

 

x+y = 50

30+y = 50

      y = 20

 

Car 1 consumes 30 gallons of gas.

Car 2 consumes 20 gallons of gas.

Answer 2

Given: Car 1: Fuel Economy FE1=35 mpg; Car2: FE2=40 mpg. Total distance traveled: D1+D2 = 1850 miles. Total gas consumption: F1+F2 = 50 gallons.

Sought: Fuel consumption per car

 

Solution:Formula: FE=D/F --> D=F*FE

D1=F1*FE1=35F1; D2=F2*FE2=(50-F1)*FE2=40(50-F1)

D1+D2=35F1+2000-40F1=-5F1+2000=1850 --> F1=(2000-1850)/5=150/5=30 gallons

F2=50-F1=50-30=20 gallons

 

Answer: The first car used up 30 gallons and the second one 20 gallons of gas during the trip.

 

Cheers,

Alex