The speed of a motor boat in still water is 20 km/h. It travels 150 km downstream and then returns to the starting point. If the round trip takes a total of 16 hours, what is the speed (in km/h) of the flow of river?
Answer & explanation
Correct answer: option 3
We know that,
When going downstream, the speed of the boat and the flow of the river are added to calculate the net speed.
When going upstream, we take the difference between the speed of the boat and the flow of the river as the net speed.
Time = Distance / Speed
(A + B) (A - B) = A2 - B2
We have,
The boat takes 16 hours to 150 km downstream and 150 km upstream.
Speed of the motorboat in the still water = 20 kmph
Let the flow of the river be R kmph.
According to the question,
{150 / (20 + R)} + {150 / (20 - R)} = 16
= {150 × (20 + R + 20 - R)} / (202 - R2) = 16
= (150 × 40) / (202 - R2) = 16
= 400 - R2 = 375
= R2 = 25
= R = 5