Multiple choice

Sophie is riding a motorboat. She rides 80 miles upstream at an average speed of x miles per hour. During downstream ride, her speed is (x + 2) miles per hour while the distance is the same. If the upstream ride took 2 hours longer than the downstream ride, how many hours did Sophie take to ride downstream?

  1. 8 hours

  2. 9 hours

  3. 10 hours

  4. 11 hours

  5. 12 hours
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A Correct answer
Explanation

Upstream time = 80/x, Downstream time = 80/(x+2). 80/x - 80/(x+2) = 2. 40/x - 40/(x+2) = 1. 40(x+2-x) = x(x+2). x^2 + 2x - 80 = 0. (x+10)(x-8) = 0. x=8. Downstream time = 80/(8+2) = 8 hours.

AI explanation

Let the downstream time be t hours; the upstream time is t plus 2, and since the distances are equal, we can equate their speeds multiplied by time. This gives x multiplied by (t plus 2) equals (x plus 2) multiplied by t, which simplifies to 2t equals x plus 2. Substituting x equals 2t minus 2 into the speed ratio gives a quadratic equation where the valid solution for the downstream time is 8 hours.

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