A man rows to a place 48 km distant and come back in 14 hours . He finds that…
2023
A man rows to a place 48 km distant and come back in 14 hours . He finds that he can row 4 km with the stream in the same time as 3 km against the stream . The rate of the stream is -
- A.
1 km/hr
- B.
1.5 km/hr
- C.
2 km/hr
- D.
2.5 km/hr
Attempted by 3 students.
Show answer & explanation
Correct answer: A
Let the boat speed in still water = x km/hr and the stream speed = y km/hr.
From the round trip: time downstream + time upstream = 48/(x+y) + 48/(x-y) = 14.
From the short-distance condition: 4/(x+y) = 3/(x-y). Solving gives 4(x - y) = 3(x + y) ⇒ x = 7y.
Substitute x = 7y into the time equation: 48/(8y) + 48/(6y) = 14 ⇒ 6/y + 8/y = 14 ⇒ 14/y = 14 ⇒ y = 1 km/hr.
Therefore the rate of the stream is 1 km/hr.