The speed of a boat in still water is 15 km/hr. It goes 30 km upstream and returns downstream to the original point in 4 hours 30 minutes. Find the speed of the stream.
Given :
Speed of boat in still water =15 km/hr
Let x be speed of the stream in km/hr
Speed of the boat upstream =15−x
Speed of the boat down stream =15+x
Time taken for upstream T1=3015−x
Time taken for downstream T2=3015+x
Given, T1+T2=92
=3015−x+3015+x=92
=30(115−x+115+x)=92
=30(15+x÷15−x(15−x)(15+x))=92
=30×30225−x2=92
=100225−x2=12
⇒225−x2=200
⇒x2=25
⇒x=5 ....(∵x is +ve)
⇒x=5 km/hr
Speed of the stream =5 km/hr.