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Between the cities A and B on the straight line there is city C. $|AC|= 180 \text{ (km)}, |BC| = 120 \text{ (km)}$.


Between A and C and B and C there are cars going back and forth with the speed $60 \text{ (km/h)}$. Two cars start at the same time from C, each one moving to a different direction (one to B and the other one to A). How much time it will take them to meet each other for the first time in C?

What is the algebraic way of the solution? I can't figure it out.

The answer is: after $12$ hours.

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up vote 1 down vote accepted

It takes $180\times 2/60 = 6$ hours for a round trip between A and C. Between B and C it's $4$ hours. The questions boils down to find out the least common multiple number of $4$ and $6$.

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Oh, that easy. Thank you very much, sir. – artyh Nov 14 '12 at 15:12

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