How many gallons were consumed by each of the two cars that week?

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 30

 miles per gallon of gas. During one particular week, the two cars went a combined total of 1925

 miles, for a total gas consumption of 60

 gallons. How many gallons were consumed by each of the two cars that week?

Answer 1

Car A: 35 mpg Car B: 30 mpg Car A travels A miles; Car B travels B miles.

A miles + B miles = 1,925 miles. Also, total gas used = 60 gal.

Mpg = miles/gal so gal = miles/mpg

Car A used A/35 gals; Car B used B/30 gals. So A/35 + B/30 = 60 But B = (1925 - A) miles

Substituting: A/35 + (1925 - A)/30 = 60

It turns out that the LCD of 35 and 30 is 210, so need to create new fractions with 210 as CD.

A/35 = 6A/210; (1925 - A)/30 = 7(1925 - A)/210 -> 6A/210 + 7(1925 - A)/210 = 60

(6A + 13475 - 7A)/210 = 60 -> -1A + 13475 = 12600 after mult both sides by 210.

-1A = 12600 - 13475 -> -1A = -875 or A = 875 mi. So Car A used 875/35 = 25 gal

Car B went 1925 - 875 = 1050 miles , so it used 1050/30 = 35 gal.

Check: 25 gal + 35 gal = 60 gal.