SOLUTION: A car gets 30 miles to the gallon of gas on the highway and 20 miles to the gallon for local driving. In the first week of October, the car was driven 180 miles on the highway, if

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Question 207010: A car gets 30 miles to the gallon of gas on the highway and 20 miles to the gallon for local driving. In the first week of October, the car was driven 180 miles on the highway, if the car's average gas mileage for that week was 26 miles to the gallon how many miles of local driving was the car used for that week?
Found 2 solutions by checkley77, MathTherapy:
Answer by checkley77(12844) (Show Source):
You can put this solution on YOUR website!
180/26=X/30+(180-X)/20
180/26=(20X+30(180-X))/30*20
180/26=(20X+5400-30X)/600
180/26=(5400-10X)/600
26(5400-10X)=600*180
140,400-260X=108,000
-260X=108,000-140,400
-260X=-32,400
X=-32,400/-260
X=124.6 MILES @ 30 MPH.
180-124.6=55.4 MILES @ 20 MPH. OF LOCAL DRIVING.
PROOF:
180/26=124.6/30+55.4/20
6.923=4.153+2.77
6.923=6.923

Answer by MathTherapy(10552) (Show Source):
You can put this solution on YOUR website!
Let the amount of local miles traveled during the 1st week of October be L

Then the total amount of miles traveled in that 1st week is 180 + L

Then the amount of gas used to travel locally is , since the car
gives 20 miles per gallon, locally

And, the total amount of gas utilized that week was: or

Therefore, (total amount of miles traveled) / (total amount of gas utilized) = average weekly consumption, or: = =

3600 + 20L = 26L + 3120

-6L = - 480

L = 80

Therefore, the amount of local miles driven was:

Check:
Total miles driven in 1 st week = 260 (180 highway + 80 local)
Total gas utilized in 1st week: 10 (6 highway + 4 local)
It follows that average gas consumption for 1st week was . or 26