SOLUTION: 1) Two dogs run around a circular track 300 feet long. One dog runs at a steady rate of 15 feet per second, the other at a strady rate of 12 feet per second. Suppose they start a

Algebra ->  Test -> SOLUTION: 1) Two dogs run around a circular track 300 feet long. One dog runs at a steady rate of 15 feet per second, the other at a strady rate of 12 feet per second. Suppose they start a      Log On


   

Question 583155: 1) Two dogs run around a circular track 300 feet long. One dog runs at a steady rate of 15 feet per second, the other at a strady rate of 12 feet per second. Suppose they start at the same point and time. What is the least number of seconds that will elapse before they are again together at the starting point?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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1) Two dogs run around a circular track 300 feet long.
One dog runs at a steady rate of 15 feet per second, the other at a steady rate of 12 feet per second.
Suppose they start at the same point and time.
What is the least number of seconds that will elapse before they are again together at the starting point?
:
Find how long it takes for each to circle the track once
Dog 1: 300%2F15 = 20 seconds
Dog 2: 300%2F12 = 25 seconds
;
Find the Least Common multiple of 20 and 25
Prime factor each
2*2*5
5*5
therefore
2*2*5*5 = 100 is the LCM
:
The will both be at the starting point in 100 seconds
:
Dog 1 will have circled it exactly 5 times
Dog 2 will have circled it exactly 4 times