In a race of 1000 meters, A beats B by 200 meters and A beats C by 500 meters. Assuming that the contestants run at constant speeds, by how many meters does B beat C?

(A) 300 (B) 375 (C) 450 (D) 500 (E) 625

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- Feb 8th 2010, 09:35 AMsri340race problem
In a race of 1000 meters, A beats B by 200 meters and A beats C by 500 meters. Assuming that the contestants run at constant speeds, by how many meters does B beat C?

(A) 300 (B) 375 (C) 450 (D) 500 (E) 625 - Feb 8th 2010, 09:52 AMArchie Meade
A speed =

B speed =

C speed =

After t, B has 200 metres to travel, an extra quarter of his distance already travelled in t (not a fifth of 1000, it's a quarter of 800).

This will take him an extra

In , C will have travelled a quarter of 500,

which is 125 metres.

Therefore C still has 1000-(500-125) metres to travel, when B crosses the line. - Feb 8th 2010, 02:14 PMSoroban
Hello, sri340!

Another approach (very primitive) . . .

Quote:

In a 1000-m race, beats by 200 meters and beats by 500 meters.

Assuming that the contestants run at constant speeds, by how many meters does beat ?

. .

The race ended like this:Code:`C B A`

+ - - - - - - - - - o - - - - - o - - - o

0 500 800 1000

ran 500 m in the time that ran 800 m.

C's speed is of 's speed.

When ran his last 200 m, ran only: . m.

As crosses the finish line, is at the 625-m mark.

Therefore, beats be 375 m . . .*answer (B).*