SOLUTION: Two kids traveled to a nearby playground on their bikes. They decided to ride back and forth across the playground. Both of them rode at a constant but different speed and they eac

Question 868549: Two kids traveled to a nearby playground on their bikes. They decided to ride back and forth across the playground. Both of them rode at a constant but different speed and they each take no time to turn around. Roman starts at the west end and Jems starts at the east end. They start at the same time and ride towards each other. They meet and pass each other 30ft from the east end.
When they reached the opposite end of the playground they turn around and ride back towards each other. When they meet again at 14 ft from the west end
What is the length of the playground?

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
= length of the playground, in feet
When Roman and Jems first meet and pass each other 30ft from the east end,
Jems has covered feet, and Roman has covered feet.
When Roman and Jems meet again at ft from the west end,
Jems has covered feet, while Roman is feet short of 2 playground lengths,
meaning that Roman has covered feet.
Since each of them rode at a constant speed,
the ratio of their speeds and the ratio of the distances covered each time they meet is always the same,
so .
We solve that equation to get :

is a solution of that equation, but it does not make sense.
is the solution that makes sense.
The length of the playground is feet.
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