Multiple choice

A motorboat takes 6 hours to cover 100 km downstream and 30 km upstream. If the boat goes 75 km downstream and returns back to starting point in 8 hours, the speed of the boat in still water is:

  1. 22 km/hr

  2. 20 km/hr

  3. 24 km/hr

  4. 30 km/hr
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let boat speed be b and stream speed be s. 100/(b+s) + 30/(b-s) = 6. 75/(b+s) + 75/(b-s) = 8. Let u = 1/(b+s) and v = 1/(b-s). 100u + 30v = 6 and 75u + 75v = 8. Solving gives b = 20, s = 5.

AI explanation

Let the speed of the boat in still water be x km/hr and the speed of the stream be y km/hr. Using the formula Time = Distance / Speed, we get the equations 100 / (x + y) + 30 / (x - y) = 6 and 75 / (x + y) + 75 / (x - y) = 8. Testing the given option of 20 km/hr for x and substituting it into the first equation results in 100 / (20 + y) + 30 / (20 - y) = 6, which simplifies to 2000 - 100y + 600 + 30y = 2400 - 6y^2. Solving this gives 6y^2 - 70y + 200 = 0, meaning y = 5 km/hr. Replacing y with 5 in the second equation confirms 75 / 25 + 75 / 15 = 3 + 5 = 8 hours. The speed of the boat in still water is 20 km/hr.

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