SOLUTION: When Frank Gresham drove 150 miles in the city, the fuel efficiency rating for his car was 18 miles/gallon. For highway driving, the fuel efficiency rating is 24 miles/gallon. How

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Question 438390: When Frank Gresham drove 150 miles in the city, the fuel efficiency rating for his car was 18 miles/gallon. For highway driving, the fuel efficiency rating is 24 miles/gallon. How far will Frank have to drive on the highway for his car to have a fuel efficiency rating of 20 miles/gallon.
My teacher gave us this problem to work on over break and he gave us the answer of 100 miles but i dont know how to get there. I checked this website and the problem has already been answered but in the explanation it says 24 - 20 is 3 which it is obviously not so i still need help setting up the problem. thank you :D

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let d = highway miles he has to drive
In words:
(total miles driven)/(gallons used) = efficiency in mi/gal
-------------
given:
Gallons of gas used in city = +150%2F18+=+25%2F3+
Gallons of gas used on highway = +d%2F24+
+%28150+%2B+d%29%2F%28+25%2F3+%2B+d%2F24+%29+=+20+
+%28150+%2B+d%29+%2F+%28%28200+%2B+d%29%2F24%29+=+20+
Multiply both sides by ++%28%28200+%2B+d%29%2F24%29+
+150+%2B+d+=+%285%2F6%29%2A%28200+%2B+d%29+
Multiply both sides by 6
+900+%2B+6d+=+1000+%2B+5d+
+d+=+1000+-+900+
+d+=+100+
He has to drive 100 miles on the highway
check answer:
+%28150+%2B+d%29+%2F+%28%28200+%2B+d%29%2F24%29+=+20+
+%28150+%2B+100%29+%2F+%28%28200+%2B+100%29%2F24%29+=+20+
+250+%2F+%28300%2F24%29+=+20+
+250+=+%2820%2F24%29%2A300+
+24%2A250+=+6000+
+6000+=+6000+
OK