Multiple choice

A, B and C take part in a race over a distance of d metres at uniform speed. If A can beat B by 20 metres, B can beat C by 10 metres and A can beat C by 28 metres, then what is the value of d?

  1. 50 metres

  2. 75 metres

  3. 100 metres

  4. 120 metres

  5. 150 metres
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A/B = d/(d-20), B/C = d/(d-10). A/C = A/B * B/C = d^2 / ((d-20)(d-10)). Given A/C = d/(d-28). So, d/(d-28) = d^2 / (d^2 - 30d + 200). Solving for d: d^2 - 30d + 200 = d^2 - 28d. 2d = 200, d = 100.

AI explanation

In a race of d metres, the ratio of the speed of A to B equals d divided by (d minus 20), and the ratio of the speed of B to C equals d divided by (d minus 10). Since A beats C by 28 metres, the ratio of the speed of A to C equals d divided by (d minus 28). Multiplying the first two ratios and setting them equal to the third gives d squared equals (d minus 20) times (d minus 10) times d divided by (d minus 28), which simplifies to 28d equals 20 times (d minus 10), yielding d equals 100. The result is 100 metres.

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