Question 1163287: Hi
A car averages 20miles a gallon of gas for city driving and 30miles a gallon for highway driving. If the average for both kinds of driving was 25miles a gallon and if 6000miles were driven how many miles were were driven in the city.
Thanks
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you would solve this by looking at the number of gallons consumed driving in the city number of gallons consumed driving on the highway.
your equations are:
c + h = 6000
c/20 + h/30 = 6000/25
c is the number of miles driven in the city.
h is the number of miles driven on the highway.
multiply both sides of the second equation by 20 * 30 = 600; simplify, and leave the first equation as is to get:
c + h = 6000
30 * c + 20 * h = 144,000
multiply both sides of the first equation by 30 and leave the second equation as is to get:
30 * c + 30 * h = 180,000
30 * c + 20 * h = 144,000
subtract the second equation from the first to get:
10 * h = 36,000
solve for h to get:
h = 3600
since c + h = 6000, then you get:
c = 2400
h = 3600
the number of gallons consumed driving in the city are 2400/20 = 120.
the number of gallons consumed driving on the highway are 3600/30 = 120.
total gallons consumed are 240.
average miles per gallon for the whole trip are 6000/240 = 25.
solution looks good, and is:
2400 miles were driven in the city.
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