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.

Explanation

Let, speed of water be x km/hr.
Given speed of motor boat in still water is 15 km/hr.
Therefore, its speed downstream is (15+x) km/hr and the speed upstream is (15-x) km/hr.
Time taken for going 30 km downstream `=(30)/(15+x)` hours.
Time taken for going 30 km upstream `=(30)/(15-x)` hours.
According to given condition
`(30)/(15+x)+(30)/(15-x)=4+(30)/(60)`
`implies(30(15-x)+30(15+x))/((15+x)(15-x))=(9)/(2)`
`implies(450-30x+450+30x)/(225-x^(2))=(9)/(2)`
`implies900xx2=9(225-x^(2))`
`implies1800=2025-9x^(2)`
`implies9x^(2)=225orx^(2)=25`
`impliesx=+-5`
`impliesx=5" "(because "speed cannot be negaitve")`
Hence, the speed of water is 5 km/hr.