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# A and B are two diametrically opposite points on a circular

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Manager
Joined: 28 Jun 2004
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A and B are two diametrically opposite points on a circular [#permalink]  18 Aug 2004, 14:59
A and B are two diametrically opposite points on a circular road whose circumference is 6 km long. A cyclist started from point A and made two circles. He made the first circle with a certain uniform speed and then decreased his speed by 3 km/hr. The interval between his two circles through point B is 50 minutes. Find the speed at which the cyclist made the first circle.
Manager
Joined: 16 May 2004
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Cyclist travels from pt b to pt a at a speed of X km/hr the he travels at X-3 km/hr since total time taken is 50 mins or 50/60 hr

3/X + 3/X-3 = 5/6
solving for x we get 9km/r.
GMAT Club Legend
Joined: 07 Jul 2004
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The time laspe will be the total time taken to travel:

From point B back to point A on the first round = 3/x (where x is the uniform speed for the first round)
And From point A back to point B on the second lap = 3/x-3

So 3/x + 3/x-3 = 50/60
So just solve the quadractic eqn to get x
Director
Joined: 20 Jul 2004
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smandalika wrote:
3/X + 3/X-3 = 5/6
solving for x we get 9km/r.

Sorry if this sounds silly, but can you post how you solved this eqn. I took hell lot of time and ended up using the big formula. Is there an easy way to solve this?
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yes, it would be easier if you drew a diagram first, then you can see it clearly. I'm having trouble attaching a diagram, will try again later.
CIO
Joined: 09 Mar 2003
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smandalika wrote:
Cyclist travels from pt b to pt a at a speed of X km/hr the he travels at X-3 km/hr since total time taken is 50 mins or 50/60 hr

3/X + 3/X-3 = 5/6
solving for x we get 9km/r.

This is exactly right.

For the record, it's important to point out that on the test, there would be five answer choices. With complicated rate problems, plugging in the answers is nearly always a great way to go, especially in a problem like this. Even if the math makes no sense, you could start with 9 km/hr, figure out how long it takes to go the first three km, and then do the same with 6 km/hr, and the answer would be 50 min.

No other answer would make that work, and it would probably take less time than figuring out the math.
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