A person rowing at the rate of 5km/h in still water, takes thrice as much time in going 40km upstream as in going 40km downstream. Find the speed of stream.
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Let the speed of the stream = x km/hr.Then the speed of the boat in downstream = (5 + x)km/hr.
Then the speed of the boat in upstream = (5 - x)km/hr.
Given that Distance = 40km.
Then the time is taken in downstream = 40/(5 + x)
Then the time is taken in upstream = 40/(5 - x).
Given that the Upstream time = 3 * Downstream Time
40/(5 - x) = 3 * 40/(5 + x)
5 + x = 3(5 - x)
5 + x = 15 - 3x
5 + x - 15 = -3x
-10 + x = -3x
x = -3x + 10
4x = 10
x = 10/4
x = 2.5.
Therefore the speed of the stream = 2.5km/hr.
Hope this helps!
Speed of the Boat downstream = (5+x) km/hr
Speed of the Boat upstream= (5-x) km/hr
Given that Distance = 40km
Time = Distance/Speed
Time taken (Downstream) =
Time taken (Upstream) =
Given that Upstream time = 3 × Downstream
40/5 - x = 3 × 40/5 + x
(40/40 gets cancelled)
5 + x = 3 ( 5 - x )
5 + x = 15 - 3x
3x + x = 15 - 5
4x = 10
Therefore, x = 10/4 = 2.5 km/hr
Therefore, SPEED of the stream = 2.5 kmph.
Hope this helps!