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. 

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 = 3hours 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` 

⇒ `81-x^2=72` 

⇒ ` 81-x^2-72=0` 

⇒ `x^2+9=0` 

⇒ `x^2=9` 

⇒ `x=3 or x=-3` 

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