question on codeforces problem I was unable to solve this problem from a past programming contest I did. Since this is more of a math question than programming, I thought it best to ask it here instead of over at stackoverflow. In the explanation on the samples (see Note at the bottom of that link), I do not know how they are getting 510.5 for the time that the second trolleybus catches up with the first. I do not have any physics background, but the physics formulas I know so far are: dist = initialVelocity * tm + .5 * acceleration * (tm*tm) time = sqrt(dist / (.5 * acceleration)) vel = initialVelocity + tm * acceleration So for the first example, trolley 1's maximum speed is 10. Max acceleration for all trolleys is 10. But I don't know how to figure out when trolley 1 and trolley 2 meet. The problem analyses for this problem is here. (see 167A at that link). But I do not understand how they are coming up with those formulas. Thanks for any help.

You don't need to find where two bus meet, try to find each bus arrival time $a_i$ if each bus can ride in his own track, then the arrival time in the complete problem is $\max_{j<=i} a_j$.

For finding the arrival bus in the simpler problem, you need to consider two subcase: the bus keep accellerating for the whole time or not?