SOLUTION: A car gets 17 mpg in the city & 30 mpg on the highway. Say I used 10.636 gallons of gas and got an average of 19 mpg for the trip. How many miles were driven in city and how many i

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Question 829809: A car gets 17 mpg in the city & 30 mpg on the highway. Say I used 10.636 gallons of gas and got an average of 19 mpg for the trip. How many miles were driven in city and how many in highway?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Recognize this as uniform rates and R*v=u where R is fuel efficiency miles per gallon, v is gallons, u is miles.

_____________Rate____________gallons volume____________miles distance
City__________17______________(____)____________________(____)
HWay__________30______________(____)____________________(____)
Total____avg, 19_______________10.636___________________(____)

Begin fillin in what you can:

_____________Rate____________gallons volume____________miles distance
City__________17______________(____)____________________(____)
HWay__________30______________(____)____________________(____)
Total____avg, 19_______________10.636___________________(19*10.636=202.084)

Obviously two sums should be formed for the two "totals". Let us use x and y for the gallon volumes as shown next:

_____________Rate____________gallons volume____________miles distance
City__________17______________(x)____________________(17x)
HWay__________30______________(y)____________________(30y)
Total____avg, 19_______________10.636___________________(19*10.636=202.084)


SYSTEM OF EQUATIONS:
------------------------------
fuel equation
------------------------------
miles equation
------------------------------

Solve that system and you will have the volume of fuel used in each of City and Highway driving for the trip, and from x and y, compute the miles for City and Highway.

Choose whichever method you like for solving the system.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

A car gets 17 mpg in the city & 30 mpg on the highway. Say I used 10.636 gallons of gas and got an average of 19 mpg for the trip. How many miles were driven in city and how many in highway?
C, or distance driven in city:  , or  miles 

Distance driven on highway:     202.084 – 152.995, or  miles

You can do the check!! 



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