Multiple choice

A boat goes 21 miles upstream and 42 miles downstream in 13 hours. It also goes 36 miles upstream and 49 miles downstream in 19 hours. What is the speed of the stream and that of the boat?

  1. 6 mph and 3 mph

  2. 5 mph and 3 mph

  3. 5 mph and 2 mph

  4. 4 mph and 2 mph

  5. None of these
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C Correct answer
AI explanation

Let the upstream speed be u and the downstream speed be d. From the given conditions, 21 divided by u plus 42 divided by d equals 13, and 36 divided by u plus 49 divided by d equals 19. Multiplying the first equation by 12 and the second by 7, then subtracting the second from the first, eliminates u and results in 168 divided by d equaling 24, meaning d equals 7 mph. Substituting 7 for d in the first equation gives 21 divided by u equals 7, so u equals 3 mph. The speed of the boat in still water is (7 plus 3) divided by 2, equaling 5 mph, and the speed of the stream is (7 minus 3) divided by 2, equaling 2 mph. The result is 5 mph and 2 mph.

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