The speed of a boat in still water is 15 km/hr. It can go 30 km upstream and return downstream to the original point in 4 hours 30 minutes. Find the speed of the stream.

Answer

5 km/hr

Explanation

Let the speed of the stream be x km/hr.
Time to go 30 km upstream `=(30km)/((15-x)km)hr=(30)/((15-x))hr.`
Time to go 30 km downstream `=(30km)/((15+x)km)hr=(30)/((15+x))hr.`
`:." "(30)/((15-x))+(30)/((15+x))=4(1)/(2)=(9)/(2)`
`implies30(15+x)+30(15-x)=(9)/(2)(225-x^(2))`
`implies450+30x+450-30x=(9)/(2)(225-x^(2))`
`implies200=225-x^(2)impliesx^(2)=25impliesx=5.`