Multiple choice

A boat travels upstream from A to B and comes back downstream from B to A in 5 hours and 20 minutes. B is the midpoint of the distance AC. Find the time taken by the boat to travel back from C to A, if it takes 6 hours to travel from A to C going upstream.

  1. 4 hours

  2. 1 hour and 20 minutes

  3. 3 hours and 40 minutes

  4. 4 hours and 40 minutes

  5. 3 hours
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D Correct answer
Explanation

Let v be boat speed and u be stream speed. Upstream time A to C is 6 hours, so AC = 6(v-u). Since B is the midpoint, AB = BC = 3(v-u). Upstream A to B is 3 hours, so downstream B to A is 5h 20m - 3h = 2h 20m. Downstream speed is BC/time = 3(v-u) / (7/3) = 9(v-u)/7. Downstream time C to A is AC / (downstream speed) = 6(v-u) / (9(v-u)/7) = 42/9 = 4 hours 40 minutes.

AI explanation

The total upstream distance from A to C is 6 hours multiplied by the upstream speed, so let the distance from A to B be x, making the distance from A to C equal to 2x. Since the boat takes 6 hours to travel from A to C upstream, it takes 3 hours to travel from A to B upstream. The round trip from A to B and back takes 5 hours and 20 minutes, which is 16/3 hours, so the downstream trip from B to A takes 16/3 minus 3, equaling 7/3 hours. Because the distance from C to A is 2x, which is twice the distance from B to A, the downstream time from C to A is twice 7/3 hours. The result is 4 hours and 40 minutes.

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