Four cars travel at constant speed along a road. Three of them (A, B and C) travel in one direction, and the fourth, D, in the opposite direction.

Car A passes B and C at 9:00h and 10:00h, respectively, and crosses car D at 11:00h.

Car D crosses car B and car C at 13:00h and 15:00h, respectively.

At what time did car B pass car C?

Bonus point: can you solve this geometrically?

At time 9:00 let cars A and B be at point P,
car C at point Q, and car D at point R.

Let a, b, c, and d be the speeds of cars
A, B, C, and D respectively.

At 10:00: a = |PQ| + c

At 11:00: 2a = |PQ| + |QR| - 2d

At 13:00: 4b = |PQ| + |QR| - 4d

At 15:00: 6c = |QR| - 6d

At time t: b(t-9) = |PQ| + c(t-9)

Solving for t we get

   35/3 or 11:40

Posted by Bractals on 2008-06-09 18:37:04