SOLUTION: A horse can run 1 1/4 miles in the same time as a man can run 1/2 mile. If the horse and the man both start from the same place on a circular track of length 1 1/2 miles, what is t

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Question 470429: A horse can run 1 1/4 miles in the same time as a man can run 1/2 mile. If the horse and the man both start from the same place on a circular track of length 1 1/2 miles, what is the least number of circuits the horse must run before both horse and man arrive simultaneously back at the starting point?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A horse can run 1 1/4 miles in the same time as a man can run 1/2 mile.
If the horse and the man both start from the same place on a circular track of length 1 1/2 miles,
what is the least number of circuits the horse must run before both horse and man arrive simultaneously back at the starting point?
:
Ratio of the horses speed to the man's speed using integers
1.25%2F.5+=+2.5%2F1+=+5%2F2
Assume:
5 mph the horses speed
2 mph the man's speed
:
Find the time in minutes for each to make one lap on the 1.5 mi track
1.5%2F5 * 60 = 18 min for the horse to complete one lap
1.5%2F2 * 60 = 45 min for the man to complete one lap
:
Find the Least common multiple of 18 and 45
Prime factor
18: 2 * 3 * 3
45: 3 * 3 * 5
LCM: 2*3*3*5 = 90 min
:
The horse will complete exactly 90%2F18 = 5 laps, least number for the horse
:
(the man will complete exactly 90%2F45 = 2 laps)