Question

A motorboat whose speed is 9 km/hr in still water, goes 15 km downstream and comes back in a total time of 3 hours 45 minutes. Find the speed of the stream. 

A motor boat whose speed in still water is 9 km/hr, goes 15 km downstream and comes back to the same spot, in a total time of 3 hours 45 minutes. Find the speed of the stream.

Answer 1

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

∴ Downstream speed = (9 + x) km/hr. 

Upstream speed = (9 – x) km/hr

Distance covered downstream = Distance covered upstream = 15 km 

Total time taken = 3 hours 45 minutes 

= `(3+45/60)` minutes 

= `225/60` minutes 

= `15/4` minutes 

∴ `15/((9 + x)) + 15/((9 - x)) = 15/4` 

⇒ `1/((9 + x)) + 1/((9 - x)) = 1/4` 

⇒ `(9 - x + 9 + x)/((9 + x)(9 - x)) = 1/4` 

⇒ `18/(9^2 - x^2) = 1/4` 

⇒ `18/(81 - x^2) = 1/4` 

⇒ 81 – x² = 72 

⇒ 81 – x² – 72 = 0 

⇒ –x² + 9 = 0 

⇒ x² = 9 

⇒ x = 3 or x = –3 

The value of x cannot be negative; therefore, the speed of the stream is 3 km/hr.