SOLUTION: Samuel has found that his new car gets 37 miles per gallon on the highway and 30 miles per gallon in the city. He recently drove 365 miles on 11 gallons of gasoline. How many miles

Question 658940: Samuel has found that his new car gets 37 miles per gallon on the highway and 30 miles per gallon in the city. He recently drove 365 miles on 11 gallons of gasoline. How many miles did he drive on the highway? How many miles did he drive in the city?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
37 mpg highway
30 mpg city.
drove 365 miles
consumed 11 gallons.
average mileage is 365/11 = 33.18181818 mpg overall average.
let x represent number of city gallons consumed.
let y represent number of highway gallons consumed.
you get the following equation:
x + y = 11
since he is getting 37 miles per gallon of x and 30 miles per gallon of y, then the total highway and city miles traveled would be found by the following equation:
37x + 30y = 365
you have 2 equations that need to be solved simultaneously.
they are:
x + y = 11
37x + 30y = 365
multiply both sides of the first equation by 30 to get:
30x + 30y = 330
subtract 30x + 30y = 330 from 37x + 30y = 365 to get:
7x = 35
solve for x to get x = 5
since x + y = 11, this means that y = 6
he consumed 5 gallons in highway driving and 6 gallons in city driving.
he drove 37 * 5 = 185 miles on the highway
he drove 30 * 6 = 180 miles in the city.
total miles is 185 + 180 = 365 which was the total miles he drove.
total gallons is 5 + 6 = 11
his average miles per gallon became 365/11 = 33.18181818 which is equivalent to 33 + 2/11 miles per gallon.

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