Multiple choice

A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is:

  1. 2mph

  2. 2.5mph

  3. 3mph

  4. 3.2mph

  5. 3.5mph
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let s be the speed of the stream. Downstream speed = 10+s, upstream = 10-s. Time difference = 36/(10-s) - 36/(10+s) = 1.5 hours (90 mins). 36(10+s - (10-s)) / (100-s^2) = 1.5 => 72s / (100-s^2) = 1.5 => 48s = 100 - s^2 => s^2 + 48s - 100 = 0. Solving gives (s+50)(s-2) = 0. Speed s = 2 mph.

AI explanation

Let the speed of the stream be x mph; the upstream speed is 10 - x and the downstream speed is 10 + x. The 90-minute difference equals 1.5 hours, so the time equation is 36 divided by (10 - x) minus 36 divided by (10 + x) equals 1.5. Cross-multiplying yields 72x equals 1.5 multiplied by (100 - x squared), which simplifies to x squared plus 48x minus 100 equals 0. Factoring this quadratic equation gives x equals 2 mph.

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