Question

A person, rowing at the rate of 5 km/h in still water, takes thrice as much time in going 40 km upstream as in going 40 km downstream. Find the speed of the stream.

Answer 1

Let the speed of the stream be v km/h

Given that, speed of a person rowing in still water = 5 km/h

The speed of a person rowing in downstream = (5 + v) km/h

And the speed of a person has rowing in upstream = (5 – v) km/h

Now, the person takes time to cover 40 km downstream,

t₁ = `40/(5 + v)` hours   ...`[because "speed" = "distance"/"time"]`

Now, the person takes time to cover 40 km upstream,

t₂ = `40/(5 - v)` hours

By condition,

t₂ = t₁ × 3

⇒ `40/(5 - v) = 40/(5 + v) xx 3`

⇒ `1/(5 - v) = 3/(5 + v)`

⇒ 5 + v = 15 – 3v

⇒ 4v = 10

∴ v = `10/4` = 2.5 km/h

Hence, the speed of the stream is 2.5 km/h.