Multiple choice

A professional boat rower can row a distance of 15 miles in still water in 1 hour. In a competition, he has to row to a certain point and back in running water, going in his preferred direction first. He covers a distance of 260 miles and back in 1 day and 16 hours. What could be the speed of water in the stream?

  1. 4.40 miles/h

  2. 5.48 miles/h

  3. 6.15 miles/h

  4. 7.47 miles/h

  5. 8.28 miles/h
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let v be the speed of the boat (15 mph) and s be the speed of the stream. Total time = 40 hours. Distance = 260 miles. 260/(15+s) + 260/(15-s) = 40. Simplifying: 260(15-s + 15+s) / (225-s^2) = 40; 260(30) / (225-s^2) = 40; 7800 / (225-s^2) = 40; 195 = 225 - s^2; s^2 = 30; s = sqrt(30) approx 5.477.

AI explanation

The speed of the boat in still water is 15 miles per hour, and the total time taken for the round trip of 260 miles each way is 40 hours. Using the total time formula of distance divided by downstream speed plus distance divided by upstream speed, we establish the equation 260 divided by (15 + w) plus 260 divided by (15 - w) equals 40. Solving for the stream speed w, we simplify the equation to 260 multiplied by 30 divided by (225 minus w squared), which equals 40, leading to 195 equals 225 minus w squared. This gives w squared equals 30, so the speed of the water in the stream is the square root of 30, which is approximately 5.48 miles per hour.

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