Maria can ride her bike to the library in 20 minutes. The trip home, wich is all uphill, takes her half an hour . If her rate is 8 miles per hour slower on the return trip, how far does she live from the library?
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Answer:
20 minutes = 1/3 hour
Let x = speed (in miles per hour) going to the library
Then, x - 8 = speed (in miles per hour) going home from the library
Distance = (Rate)(Time)
Since the one way distances are the same, (1/3)x = (1/2)(x-8)
Multiply through by the LCD, 6, to get 2x = 3(x-8)
2x = 3x - 24
x = 24 mph
One way distance = (1/3)x = 8 miles