alanforde800Maximus wrote:Both runners and walkers are participating in a marathon on exactly the same course. The walkers start at 6:45 AM, and the runners begin at 8:00 AM. Bill is entered as a walker and is going to walk at a constant rate of 4 miles per hour. The fastest runner is going to be running at a constant rate of 9 miles per hour. How far will Bill have walked before he is passed by the fastest runner?
a) 4 miles
b) 5 miles
c) 8 miles
d) 9 miles
e) 10.5 miles
Since Bill's rate is 4 miles per hour, the distance traveled by Bill between 6:45am and 8am = rt = (4)(5/4) = 5 miles.
Time for the runner to catch up = (distance behind)/(catch-up rate).
The CATCH-UP rate is the DIFFERENCE between the runner's rate and Bill's rate:
9-4 = 5 miles per hour.
Here is the reasoning:
Every hour the runner travels 9 miles, while Bill travels 4 miles.
Result:
Every hour the runner travels 5 MORE MILES THAN than Bill, allowing the runner to CATCH UP by 5 miles every hour.
Time for the runner to catch up = (distance behind)/(catch-up rate) = 5/5 = 1 hour.
Additional distance traveled by Bill in this hour = rt = 4*1 = 4 miles.
Thus:
Total distance traveled by Bill = 5+4 = 9 miles.
The correct answer is
D.
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