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Question
The speed of a boat in still water is 15 km/hr. It can go 30 km upstream and return downstream to the original point in 4 hours 30 minutes. Find the speed of the stream.
Solution
Let the speed of the stream be x km/hr.
∴ Speed of the boat downstream = (15 + x) km/hr
Speed of the boat upstream = (15 – x) km/hr
Time taken to go 30 km downstream = `30/(15 + x)` hr
Time taken to come back = `30/(15 - x)` hr
From the given information,
`30/(15 + x) + 30/(15 - x) = 4 30/60`
`30/(15 + x) + 30/(15 - x) = 9/2`
`(450 - 30x + 450 + 30x)/((15 + x)(15 - x)) = 9/2`
`900/(225 - x^2) = 9/2`
`100/(225 - x^2) = 1/2`
225 – x2 = 200
x2 = 25
x = ±5
But, x cannot be negative, so, x = 5.
Thus, the speed of the stream is 5 km/hr.
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