A family has two cars. During one particular week,

Question

A family has two cars. During one particular week, the first car consumed 30

 gallons of gas and the second consumed 20

 gallons of gas. The two cars drove a combined total of 950

 miles, and the sum of their fuel efficiencies was 40

 miles per gallon. What were the fuel efficiencies of each of the cars that week? 

what first car miles per gallon?

what second car miles per gallon?

Answer 1

There are two unknowns.

Let f = fuel efficiency of the first car in mpg (consumed 30 gallons)

Let s = fuel efficient of the second car in mpg (consumed 20 gallons)

Since the sum of the fuel efficiency is 40, you have f + s = 40

The number of miles driven is equal to the fuel efficiency times the number of gallons. The total gallons is 950, so you have a second equation of 30f + 20s = 950.

This give you a systems of equation

f + s = 40

30f + 20s = 950

Using the elimination method, you can multiply the first equation by -20 so it will become -20f - 20s = -800.

Adding this to the second equation will give you 10f = 150. So you get f = 15. So the fuel efficiency of the first car is 15 mpg.

Since f + s = 40, then 15 + s = 40 means that s = 25. So the second car has a fuel efficiency of 25 mpg.

Answer 2

Let x and y be the miles per gallon of car 1 and car 2 respectively. Since their combined fuel economy is 40, we have one equation of x+y=40. Then since miles per gallon of a car times the gallons of gas used gives miles driven by that car, we get the equation 30x + 20y = 950. Now solve the system of equations (I will use the addition method:

20 [x + y = 40] → 20x + 20y = -800

30x + 20y = 950

- 20x + 20y = 800

-----------------------------

10x + 0y = 150

Since 10x=150, x=15. Then since x+y=40, 15+y=40 and y=25.

Thus the miles per gallon of car 1 and car 2 are 15 and 25 respectively.

Answer 3

f =30 gal

s = 20 gal

950 = 30F +20S where

F = speed of First car,

S = speed of Second car

40 = F +S

800 = 20F +20S

150 = 10F

F = 15 mpg

S= 25 mpg

30(15) + 20(25) = 450 + 500 = 950 miles

15 +25 = 40 mpg