Multiple choice

Runners A, B and C run a race, with runner A finishing 12 metres ahead of runner B and 18 metres ahead of runner C, while runner B finishes 8 metres ahead of runner C. Each runner travels the entire distance at a constant speed. The length of the race is

  1. 36 metres

  2. 48 metres

  3. 60 metres

  4. 72 metres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let L be the race length. A beats B by 12m, so A/L = B/(L-12). A beats C by 18m, so A/L = C/(L-18). B beats C by 8m, so B/L = C/(L-8). Using the ratios, (L-12)/L = (L-18)/(L-8). Solving for L: (L-12)(L-8) = L(L-18) => L^2 - 20L + 96 = L^2 - 18L => 2L = 96 => L = 48.

AI explanation

Let the total distance of the race be D. When A finishes the race, B has run D minus 12 meters and C has run D minus 18 meters, so the ratio of the speeds of B and C is (D - 12) divided by (D - 18). When B finishes the race, C has run D minus 8 meters, meaning the ratio of the speeds of B and C is D divided by (D - 8). Equating the two ratios gives (D - 12) / (D - 18) = D / (D - 8). Solving this equation yields (D - 12)(D - 8) = D(D - 18), which expands to D squared minus 20D plus 96 equals D squared minus 18D. Solving for D gives 2D = 96, so the length of the race is 48 metres.

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