Algebra word problem?
A family has two cars. The first car has a fuel efficiency of 15 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 1725 miles, for a total gas consumption of 75 gallons. How many gallons were consumed by each of the two cars that week?
Comments
one car went x miles, the other one covered the rest = 1725-x
now for the gas consumption
let x be for the 15 mpg car
x/15 + (1725-x)/30 = 75
multiply all terms by 30 the LCD
2x + 1725-x = 2250
x = 2250-1725 = 525 miles at 15 mpg
1725-x = 1200 miles at 30 mpg
Rx= gas rate of first car in mi/gal= 15mi/gal
Ry= gas rate of second car in mi/gal=30mi/gal
x= gallons consumed by first car
y=gallons consumed by second car
Dx=distance of first car travels
Dy=distance of second car travels
Dx + Dy= 1725mi.........15x +30y=1725
x + y = 75gal..................x + y = 75
y=75-x
15x + 30(75-x)=1725
15x + 2250 - 30x = 1725
-15x=-525
x=35gal
y= 75-30=45 gal