Multiple choice

A boat can go 30 km downstream and 24 km upstream in 2 hours 27 minutes. Also, it can go 10 km downstream and 4 km upstream in 37 minutes. What is the speed of the boat upstream (in km/h)?

  1. 24

  2. 18

  3. 22

  4. 20
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let d be the downstream speed and u be the upstream speed. From the given conditions, we set up two equations: 30/d + 24/u = 147/60 and 10/d + 4/u = 37/60. Multiplying the second equation by 3 and subtracting it from the first equation eliminates d, giving 12/u = 36/60, which simplifies to an upstream speed of 20 km/h.

AI explanation

Let the downstream speed be D and the upstream speed be U. From the second condition, 10 km divided by D plus 4 km divided by U equals 37 minutes. Multiplying by 6 gives 60 divided by D plus 24 divided by U equals 222 minutes. Subtracting this from the first condition (147 minutes equals 30 divided by D plus 24 divided by U) yields a negative value, so instead multiply the second condition by 3 to get 30 divided by D plus 12 divided by U equals 111 minutes. Subtracting this from the first condition gives 12 divided by U equals 36 minutes, meaning U equals 12 divided by (36 divided by 60) hours, which equals 20 km/h. The result is 20.

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