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.

The speed of a boat in still water is 15 km/hr. It goes 30 km upstream and returns back at the same point in 4 hours 30 minutes. Find the speed of the stream.

Answer 1

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.