Question

The speed of a boat in still water is 8 km/hr. It can go 15 km upstream and 22 km downstream is 5 hours. Fid the speed of the stream

Answer 1

Speed of the boat in still water  =8 km/ hr.
Let the speed of the stream be x km/hr.   

∴Speed upstream=`(8-x)`km/hr.  

Speed downstream =`(8+x)` km/hr. 

Time taken to go 22 km downstream=`22/(8+x) hr` 

Time taken to go 15 km upstream=`15/((8-x))hr` 

According to the question: 

⇒`22/(8+x)+15/(8-x)=5` 

⇒`22/(8+x)+15/(8-x)-5=0` 

⇒`(22(8-x)+15(8+x)-5(8-x)(8+x))/((8-x)(8+x))=0` 

⇒`176-22x+120+15x-320+5x^2=0` 

⇒`5x^2-7x-24=0` 

⇒`5x^2-(15-8)x-24=0` 

⇒`5x^2-15x+8x-24=0` 

⇒`5x(x-3)-8(x-3)=0` 

⇒`(x-3) (5x-8)=0` 

⇒`x-3=0  or 5x-8=0` 

⇒`x=3 or x=8/5` 

⇒`x=3`                ( ∴Speed cannot be a fraction)
∴Speed of the stream =3 km/ hr