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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
Solution
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.
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