SOLUTION: A car traveled 262 miles on a trip. During 90 miles of the trip, the car traveled through the city and had gas mileage that was 13 fewer miles per gallon than the gas mileage on th

Question 380060: A car traveled 262 miles on a trip. During 90 miles of the trip, the car traveled through the city and had gas mileage that was 13 fewer miles per gallon than the gas mileage on the highway. If the total amount of gasoline used for the trip was 7 gallons, find the gas mileage of the car on the highway.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A car traveled 262 miles on a trip. During 90 miles of the trip, the car
traveled through the city and had gas mileage that was 13 fewer miles per
gallon than the gas mileage on the highway.
If the total amount of gasoline used for the trip was 7 gallons, find the
gas mileage of the car on the highway.
:
Let x = gas mileage on the highway
then
(x-13) = gas mileage in the city
:
Find the number of miles traveled on the highway: 262 - 90 = 172
:
gals on hwy + gals in city = 7 gallons
+ = 7
multiply equation by x(x-13), results
172(x-13) + 90x = 7x(x-13)
:
172x - 2236 + 90x = 7x^2 - 91x
:
262x - 2236 = 7x^2 - 91x
Combine like terms on the right
0 = 7x^2 - 91x - 262x + 2236
A quadratic equation
7x^2 - 353x + 2236 = 0
Use the quadratic formula to find x, a=7; b=-353; c=2236
Do the math, of the two solutions, the reasonable one:
x = 43 mpg on highway
:
:
Check this by finding the total gal
172/43 = 4
90/30 = 3
------------
total; 7 gal
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