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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.
Solution
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.
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