SOLUTION: Two runners start running at the same time from the start/finish line of a 400 meter oval track. One runner runs laps of 1 minute 15 seconds and the other runs laps of 1 minute 45

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Question 749075: Two runners start running at the same time from the start/finish line of a 400 meter oval track. One runner runs laps of 1 minute 15 seconds and the other runs laps of 1 minute 45 seconds. How long will it be before the runners cross the finish line at the same time?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Two runners start running at the same time from the start/finish line of a 400 meter oval track.
One runner runs laps of 1 minute 15 seconds and the other runs laps of 1 minute 45 seconds.
How long will it be before the runners cross the finish line at the same time?
:
Change the times to seconds:
Runner one laps in 75 sec
Runner two laps in 105 sec
:
Find the least common multiple of 75 and 105 by prime factoring.
75: 3*5*5
105: 3*7*5
LCM: 3*5*5*7 = 525 seconds they will cross the finish line at the same time
(That's 8 min 45 sec)
:
Runner one completes exactly 525/75 = 7 laps
Runner two completes exactly 525/105 = 5 laps