A motor boat goes 20 km downstream and comes back to the starting point in 6 hours. If the speed of the boat in still water is 12 km/h, then the speed of the stream is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 8 km/h
Let the speed of the stream be s km/h. Then
\(\text{downstream speed} = 12 + s\)
\(\text{upstream speed} = 12 - s\)
The total time for 20 km down and 20 km back is 6 hours:
\( \displaystyle \frac{20}{12 + s} + \frac{20}{12 - s} = 6 \)
\( \displaystyle \frac{20(12 - s) + 20(12 + s)}{144 - s^2} = 6 \)
\(480 = 6(144 - s^2)\)
\(480 = 864 - 6s^2\)
\(6s^2 = 384\)
\(s^2 = 64,\quad s = 8\)
Check: 20/20 + 20/4 = 1 + 5 = 6 hours.