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 - x²} ] = 11/4

⇒ 12 [ {22} / {121 - x²} ] = 11/4

⇒ 12 [ 2 / {121 - x²} ] = 1/4

⇒ 24 / {121 - x²}  = 1/4

⇒ 24 (4) = {121 - x²} 

⇒ 96 = 121 - x²

⇒ x² = 121 - 96

⇒ x² = 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.