A pickup truck gets 20 mpg in the city and 24 mpg on the highway. If the driver drives 310 miles on 14 gal of gas,determine the number of city miles and highway miles the truck was driven

Answer 1

C is the number of city miles

H is the number of highway miles

C+H = 310 ---> H= 310 - C

The number of gallons used in the city is C/20.

The number of gallons used on the highway is H/24.

C/20 + H/24 = 14

C/20 + (310-C)/24 = 14 <--- substitutes the first equation above in bold

24*C + (310 - C)*20 = 14*480 <--- multiplies both sides by 480, the least common denominator,

so as to cancel out the fractions

24C + 6200 - 20C = 6720 <--- distributive property

4C + 6200 = 6720 <--- combines like terms

4C = 520 <---- solves for C

C = 130

130 miles in the city ---> 130/20 = 6.5 gallons

180 miles on the highway ---> 180/24 = 90/12 = 45/6 = 15/2 = 7.5 gallons

The total is 14 gallons