Multiple choice

Three runners Dexter, Micheal and Frodo are running a race in water with Dexter finishing 20 m ahead of Micheal and 34 m ahead of Frodo, while Micheal finishes 21 m ahead of Frodo. Each of the three participants are running with a constant speed during the race. Each runner travels the entire distance at a constant speed. What was the length of the pool in which the race was taking place?

  1. 40 m

  2. 50 m

  3. 60 m

  4. 80 m

  5. 90 m
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let L be the length. Dexter finishes at L, Micheal at L-20, Frodo at L-34. When Micheal finishes at L, Frodo is at L-21. The ratio of speeds of Micheal to Frodo is L / (L-21). Also, the ratio of speeds is (L-20) / (L-34). Equating: L/(L-21) = (L-20)/(L-34). L^2 - 34L = L^2 - 41L + 420. 7L = 420, L = 60.

AI explanation

When Dexter finishes the race, Micheal is 20 m behind and Frodo is 34 m behind. Since Micheal finishes 21 m ahead of Frodo overall, Micheal needs to run those remaining 20 m while Frodo runs the final stretch to finish 21 m behind him. The ratio of their speeds is constant, so the distance Micheal runs to the distance Frodo runs in that same time is 20 to (34 - 21), which is 20 to 13. Therefore, Micheal's total race distance L is related to Frodo's distance (L - 21) by the proportion L divided by (L - 21) equals 20 divided by 13. Solving 13L = 20L - 420 gives 7L = 420, so L = 60. The length of the pool was 60 m.

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