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This problem trains for: SAT-I, AMC-8, GMAT.
A bicycle race starts in town A on the road to town B. A truck with fresh vegetables starts in town B going towards town A on the same road and starts 1 hour and 15 minutes after the race. The average speed of the truck is five times as large as that of the fastest cyclist. The truck meets the race three hours after the start of the race. If the distance between the two towns is 94 miles, what is the average speed of the fastest cyclist?
If the speed of the fastest cyclist is x, the distance traveled by the front of the race in three hours is 3x.
The distance traveled by the truck during the same three hours is:
We have converted the 15 minutes to .25 hours and we have subtracted the delay from the 3 hr time interval.
These distances must sum up to 94 miles.
Solving for x we obtain a speed of 8 mph.