Multiple choice

A boat takes $90$ minutes less to travel $36$ km downstream than to travel the same distance upstream. If the speed of the boat in still water is $10$ km/hr, then what is the speed of the stream ?

  1. $4$ km/hr
  2. $3$ km/hr
  3. $2.5$ km/hr
  4. $2$ km/hr
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let s be stream speed. Time upstream = 36/(10-s), time downstream = 36/(10+s). Given 36/(10-s) - 36/(10+s) = 1.5 hours (90 mins). Solving 36(10+s - 10+s)/(100-s^2) = 1.5 leads to 72s = 1.5(100-s^2), which simplifies to s^2 + 48s - 100 = 0. Solving gives s = 2.

AI explanation

Let the speed of the stream be x km/hr; the time difference equation is 36 divided by (10 minus x) minus 36 divided by (10 plus x) equals 1.5 hours. Multiplying by the common denominator yields 36 times (10 plus x) minus 36 times (10 minus x) equals 1.5 times (100 minus x squared). Solving 72x equals 150 minus 1.5x squared gives x equals 2 km/hr.

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