# A motorboat whose speed in still water is 18 km/h, takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find 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 6 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 18 km/hr.

Sspeed of the boat in upstream = (18 - x) km/hr

Speed of the boat in downstream = (18 + x) km/hr

It is mentioned that the boat takes 1 hour more to go 24 km upstream than to return downstream to the same spot

Therefore, One-way Distance traveled by boat (d) = 24 km

Hence, Time in hour

T_{upstream }= T_{downstream }+ 1

[distance / upstream speed ] = [distance / downstream speed] _{ }+ 1

[ 24/ (18 - x) ] = [ 24/ (18 + x) ] + 1

[ 24/ (18 - x) - 24/ (18 + x) ] = 1

24 [1/ (18 - x) - 1/(18 + x) ] = 1

24 [ {18 + x - (18 - x) } / {324 - x^{2}} ] = 1

24 [ {18 + x - 18 + x) } / {324 - x^{2}} ] = 1

⇒ 24 [ {2}x / {324 - x^{2}} ] = 1

⇒ 48x = 324 - x^{2}

⇒ x^{2} + 48x - 324 = 0

⇒ x^{2} + 54x - 6x - 324 = 0 ----------> (by splitting the middle-term)

⇒ x(x + 54) - 6(x + 54) = 0

⇒ (x + 54)(x - 6) = 0

⇒ x = -54 or 6

As speed to stream can never be negative, we consider the speed of the stream (x) as 6 km/hr.