Question

A motor boat whose speed in still water is 178 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-x^2=48x` 

⇒`324-x^2-48x=0` 

⇒`x^2+48x-324=0` 

⇒`x^2+(54-6)x-324=0` 

⇒`x^2+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.