Multiple choice

A boat goes upstream 21 miles and downstream 42 miles in 13 hours. Under identical circumstances, it also goes upstream 36 miles and downstream 49 miles in 19 hours. Find the speed of the flow of water in the stream and that of the boat in a fresh-water lake where the water is still, respectively. Both the speeds are to be determined in miles per hour.

  1. 3, 6

  2. 3, 5

  3. 2, 5

  4. 2, 4

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

Let boat speed be x, stream speed be y. Upstream speed = x-y, downstream = x+y. 21/(x-y) + 42/(x+y) = 13 and 36/(x-y) + 49/(x+y) = 19. Solving this system gives x=5, y=2.

AI explanation

Let the upstream speed be u miles per hour and the downstream speed be d miles per hour. From the given information, form the equations 21 divided by u plus 42 divided by d equals 13, and 36 divided by u plus 49 divided by d equals 19. Solving this system of equations yields u equal to 3 and d equal to 7. The speed of the boat in still water is (d + u) / 2, which is (7 + 3) / 2 = 5 mph, and the speed of the flow is (d - u) / 2, which is (7 - 3) / 2 = 2 mph. The correct speeds for the flow and the boat are 2 mph and 5 mph.

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