At the cycle track

Algebra Level 3

On a circular cycle track there are two cyclists gong at constant speeds.When they go in opposite directions, they meet every 10 seconds;when they go in the same direction, one catches up with the other every 170 seconds.Find the speed of each cyclist if the circular track is 170 meters long.

NOTE:If the speed of each cyclist is a and b respectively, then find the value of a+b.

Give your answer in meters per second.

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The answer is 17.

Anik Mandal by Anik Mandal , 21, India

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2 solutions

Janercy Deng
Jul 23, 2014

well the second condition is unnecessary. Since they meet every 10 seconds, we could say that they finish 170 meters in 10 seconds. Assume the sum of the speed of both cyclists is a + b meter / sec, then 10 (a + b) = 170, which leads to the solution, a + b = 17

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Anik Mandal
May 26, 2014

If the speed of the first cyclist is x ,Then in 10 seconds he covers a distance of 10x meters.If the other cyclist is moving towards the first one then during the time between meetings he covers the remaining portion or 170-10x meters. If the other cyclist has a speed of y Then he travels 10y meters in 10 seconds.We have

170-10x=10y

Now if the cyclists are following one another,then the first one covers 170x meters in 170 seconds,and the other one does 170y meters.If the first one is faster than the second one ,he does one complete circle more than than the second one before they meet again.WE thus have

170x-170y=170

Simplifying these equations we get,

x+y=17 and x-y=1

Hence x=9 and y=8 (meters per second)

0 Helpful 0 Interesting 0 Brilliant 0 Confused

No need to solve x and y.. you jeed just x+y. So first information is sufficient

Kushagra Jaiswal - 7 years ago

That's right! But the answer of the actual problem should be 8 and 9 (meters per second).

Anik Mandal - 7 years ago

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