SOLUTION: When Mr. Gomez drives his car to work, the trip takes 30 minutes. When he rides the bus, it takes 45 minutes. If his average driving speed is 12 mph faster than the average speed o

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Question 745124: When Mr. Gomez drives his car to work, the trip takes 30 minutes. When he rides the bus, it takes 45 minutes. If his average driving speed is 12 mph faster than the average speed of the bus, find the distance he travels to work.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the distance to work
Let +s+ = the speed of the bus
Convert minutes to hours
By car:
(1) +d+=+%28+s+%2B+12+%29%2A%281%2F2%29+
By bus:
(2) +d+=+s%2A%283%2F4%29+
------------------
Substitute (2) into (1)
(1) +s%2A%283%2F4%29+=+%28+s+%2B+12+%29%2A%281%2F2%29+
Multiply both sides by +4+
(1) +3s+=+2%2A%28+s+%2B+12+%29+
(1) +3s+=+2s+%2B+24+
(1) +s+=+24+
Substitute this result into (2)
(2) +d+=+24%2A%283%2F4%29+
(2) +d+=+6%2A3+
(2) +d+=+18+
The distance to work is 18 miles