Multiple choice

Albert can row a boat 32 km upstream and 45 km downstream in 17 hours. Also, he can row 40 km upstream and 55 km downstream in 21 hours. The speeds of the stream and the boat in still water, respectively, are

  1. 2 km/hr and 8 km/hr

  2. 1.75 km/hr and 7.25 km/hr

  3. 0.5 km/hr and 4.5 km/hr

  4. 0.5 km/hr and 4 km/hr

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let u = upstream speed, d = downstream speed. 32/u + 45/d = 17 and 40/u + 55/d = 21. Solving this system: let x=1/u, y=1/d. 32x+45y=17, 40x+55y=21. Multiplying by 5 and 4: 160x+225y=85, 160x+220y=84. So 5y=1, y=0.2, d=5. Then 32x + 9 = 17, 32x=8, x=0.25, u=4. Boat speed = (d+u)/2 = 4.5, stream = (d-u)/2 = 0.5.

AI explanation

Let the upstream speed be U and the downstream speed be D. From the given information, 32 divided by U plus 45 divided by D equals 17, and 40 divided by U plus 55 divided by D equals 21. Multiplying the first equation by 5 and the second by 4, then subtracting to eliminate the D terms, yields U equal to 4 km/hr. Substituting U back into the first equation gives D equal to 5 km/hr. The speed of the stream is (D minus U) divided by 2, which is (5 minus 4) divided by 2, resulting in 0.5 km/hr. The speed of the boat in still water is (D plus U) divided by 2, which is (5 plus 4) divided by 2, resulting in 4.5 km/hr.

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