The ratio of the speed of a motorboat to that of the speed of current is 31: 6. The motorboat starts from a point and covers a certain distance along the current in 4 h 10 min. Find the time taken by the motorboat to come back to its initial point.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 6 h 10 min.
Given that:
The speed of the motorboat/the speed of current = 31/6
The motorboat starts from a point and covers a certain distance along the current in = 4 h 10 min
Let the speed of the motorboat = 31x
Then,
The speed of water current = 6x
So,
The relative speed of the boat along the current = 31x + 6x = 37x
The relative speed of the boat against the current = 31x - 6x = 25x
According to the question:
37x × (4 + 10/60) = 25x × return time
⇒ Return time = (37 × 25)/( 6 × 25) = 6 h 10 min