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Circular cyclists

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by GmatKiss » Thu May 24, 2012 5:59 am
Two cyclists ride along a circular path whose circumference is 10 km. The two cyclists start at the same time and from same position. The first cyclist goes at a constant speed of 30 km/h in the clockwise direction, while the second goes at a constant speed of 20 km/h in the counterclockwise direction. They both cycle for 1 hour. How many times do they meet?

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by niketdoshi123 » Thu May 24, 2012 6:26 am
GmatKiss wrote:Two cyclists ride along a circular path whose circumference is 10 km. The two cyclists start at the same time and from same position. The first cyclist goes at a constant speed of 30 km/h in the clockwise direction, while the second goes at a constant speed of 20 km/h in the counterclockwise direction. They both cycle for 1 hour. How many times do they meet?

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Speed of Cyclist A (clock wise direction) = 30km/h
Speed f Cyclist B (counter clock wise direction) = 20km/h
Their relative speed = speed of A + Speed of B = 50 km/h

When they together cover a distance of 10 km they meet each other, so the time taken when they meet each other = 10/50 = .2 hr = 12 mins
this means that in every 12 mins they meet each other, so in 1 hr they will meet 5 times.
Hence the answer is
E
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by GMATGuruNY » Thu May 24, 2012 9:48 am
GmatKiss wrote:Two cyclists ride along a circular path whose circumference is 10 km. The two cyclists start at the same time and from same position. The first cyclist goes at a constant speed of 30 km/h in the clockwise direction, while the second goes at a constant speed of 20 km/h in the counterclockwise direction. They both cycle for 1 hour. How many times do they meet?

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When elements travel toward each other, they WORK TOGETHER to cover the distance between them.
Thus, we ADD THEIR RATES.
The combined rate for the two cyclists = 20+30 = 50 kilometers per hour.
Thus, in 1 hour, the cyclists will travel the 10 kilometers of the track 5 times.

The correct answer is E.
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