swerve wrote:It takes Kaya a total of 9 hours to go from home to work and back on her bike. She travels at an average speed of 5 miles per hour from home to work and twice as fast coming home than going to work. If Kaya travels by the same route in both directions then how many miles is the distance from her home to work?
A. 67.5
B. 45
C. 30
D. 18
E. 6
Time and rate have a RECIPROCAL RELATIONSHIP:
If John's time is twice Mary's time, then John's rate is 1/2 Mary's rate.
Here, the rate for the return trip is twice the rate for the trip to work, implying that the time for the return trip is 1/2 the time for the trip to work.
Since the total time for both trips is 9 hours, we get:
Trip to work = 6 hours.
Return trip = 3 hours.
Since the 6-hour trip to work is traveled at 5 mph, the distance = rt = 5*6 = 30 miles.
The correct answer is
C.
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