SOLUTION: A piece of land is 20 miles in circumference. Three persons, A, B, and C, start from the same place and travel the same way. A travels 3 mph, B 7 mph, and C 11 mph. In what time wi
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Question 1106369: A piece of land is 20 miles in circumference. Three persons, A, B, and C, start from the same place and travel the same way. A travels 3 mph, B 7 mph, and C 11 mph. In what time will they be together again?
Not sure how to solve. Non-homework. Found 2 solutions by josmiceli, ikleyn:Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website! The time has to to divisible by the times
for each one to go around once
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A's time to go around once:
B'stime:
C's time:
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The time, that is divisible by
these 3 times is: hrs
They will be togther again in 34 hrs 38 min
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Check the math and get another opinion if needed
In 5 hours person A will cover 5*3 = 15 miles.
person B will cover 5*7 = 35 miles, which is one entire circumference of 20 miles plus the same 15 miles: 35 = 20 + 15.
person C will cover 5*11 = 55 miles, which is TWO TIMES entire circumference of 20 miles plus the same 15 miles: 55 = 2*20 + 15.
So, in 5 hours all three of them will be at the same point on the circumference.
To that time person A will be on the way making his first lap;
person B will complete his first lap and will be on the way making his 2-nd lap;
and person C will complete his TWO laps and will be on the way making his 3-rd lap.
It is informal solution.
The formal solution is based on the following fact:
For two bodies that started simultaneously from one point and move uniformly along the circle (along the closed path) of
the circumference S in the same direction with different speeds/rates and , > , the time from the start till the moment
when the faster body will catch the slower body is this condition
= S: the difference between the covered distanses is exactly equal to the circumference.
It is also the condition for the time duration between any two consecutive catching moments.
