Question

A motor boat whose speed in still water is 18 km/hr, takes 1 hour more to go 24 km upstream than to return to the same spot. Find the speed of the stream.

Answer 1

Let the speed of the stream be x km/hr.

Given: 

Speed of the boat = 18 km/hr

∴ Speed downstream = (18 + x) km/hr 

Speed upstream = (18 – x) km/hr

∴ `24/((18 - x)) - 24/((18 - x)) = 1`  

⇒ `1/((18 - x)) - 1/((18 + x)) = 1/24` 

⇒ `(18 + x - 18 + x)/((18 - x)(18 + x)) = 1/24` 

⇒ `(2x)/(18^2 - x^2) = 1/24` 

⇒ 324 – x² = 48x 

⇒ 324 – x² – 48x = 0 

⇒ x² + 48x – 324 = 0 

⇒ x² + (54 – 6)x – 324 = 0 

⇒ x² + 54x – 6x – 324 = 0 

⇒ x(x + 54) – 6(x + 56) = 0 

⇒ (x + 54) (x – 6) = 0 

⇒ x = –54 or x = 6  

The value of x cannot be negative; therefore, the speed of the stream is 6 km/hr.