#### 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 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 - x^2 = 200`

`x^2 = 25`

`x = +- 5`

But, x cannot be negative, so, x = 5.

Thus, the speed of the stream is 5 km/hr.

Is there an error in this question or solution?

Solution 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. Concept: Quadratic Equations.