Discussion
A, B and C ran a 1.5 km race. A beat B by 50 seconds and B beat C by 30 seconds. Also, A beat C by 400 m. Find the time (in seconds) that A took to run the race.
Answer: B
A took 220 seconds. Let A's time be T. Then B takes T + 50 and C takes T + 80 seconds. When A finishes the 1500 m, C is 400 m behind, so C has run 1100 m in T seconds. C's speed is 1100/T, and he runs 1500 m in T + 80 seconds: \[\frac{1500}{T + 80} = \frac{1100}{T}\] \[1500T = 1100T + 88000\] \[T = 220\] Check: C covers 1100 m in 220 s, 5 m per second, and 1500 m in 300 s, which is 220 + 80. The other options give a speed that does not match this.
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