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A man can row at 9 km/hr in still water. If the stream speed is 6 km/hr and it takes him 14 hours to row to a place and back, how far is the place?

A man can row at 9 km/hr in still water. If the stream speed is 6 km/hr and it takes him 14 hours to row to a place and back, how far is the place? Correct Answer 35 km

Given:

Speed of man in still water = 9 km/h

Speed of stream = 6 km/h

Total time taken = 14 hours

Concept used:

If the speed of a boat/man in still water be x km/h and the speed of the stream be y km/h, then

Speed of boat downstream = (x + y) km/h

Speed of boat upstream = (x - y) km/h

Speed = Distance/Time

Calculation:

Let the distance traveled by man be D km and time taken be t1 in downstream and t2 in upstream

Speed of man in downstream = (x + y) km/h

⇒ (9 + 6) = 15 km/h

Time, t1 = D/15      ----(1)

Speed of man in upstream = (x - y) km/h

⇒ (9 - 6) = 3 km/h

Time, t2 = D/3      ----(2)

Adding equations (1) and (2), we get

⇒ t1 + t2 = (D/15) + (D/3)

⇒ 14 = (5D + D)/15

⇒ 14 × 15 = 6D

⇒ (14 × 15)/6 = D

⇒ 7 × 5 = D

⇒ 35 km = D

∴ The place is 35 km far away.

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