# Find Out the Speed of the Stream.

## Question: The speed of a boat in still water is 11 km/hr. It can go 12 km upstream and return downstream to its original point in 2 hr 45 min. Find out the speed of the stream.

The question is a real-life application of linear equations in two variables.

## Answer: The speed of the stream is 5 km/hr.

Let's explore the water currents.

## Explanation:

Let the speed of the stream be x km/hr

Given that, the speed boat in still water is 11 km/hr.

⇒ speed of the boat upstream = (11 - x) km/hr

⇒ speed of the boat downstream = (11+ x) km/hr

It is mentioned that the boat can go 12 km upstream and return downstream to its original point in 2 hr 45 min.

⇒ One-wayDistance traveled by boat (d) = 12 km

⇒ T_{upstream }+ T_{downstream }= 2 hr 45 min = (2 + 3/4) hr = 11/4 hr

⇒ [distance / upstream speed ] + [distance / downstream speed] _{ }= 11/4

⇒ [ 12/ (11-x) ] + [ 12/ (11+x) ] = 11/4

⇒ 12 [ 1/ (11-x) + 1/(11+x) ] = 11/4

⇒ 12 [ {11 - x + 11 + x} / {121 - x^{2}} ] = 11/4

⇒ 12 [ {22} / {121 - x^{2}} ] = 11/4

⇒ 12 [ 2 / {121 - x^{2}} ] = 1/4

⇒ 24 / {121 - x^{2}} = 1/4

⇒ 24 (4) = {121 - x^{2}}

⇒ 96 = 121 - x^{2}

⇒ x^{2} = 121 - 96

⇒ x^{2} = 25

⇒ x = + 5 or -5

As speed to stream can never be negative, we consider the speed of the stream(x) as 5 km/hr.

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

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