Question
Speed of a boat in still water is 15 km/h. It goes 30 km upstream and returns back at the same point in 4 hours 30 minutes. Find the speed of the stream.
Solution
Let the speed of the stream be x km/h.
It is given that the speed of a boat in still water is 15 km/h.
Now,
Speed of the boat upstream = Speed of the boat in still water − Speed of the stream = (15 − x) km/h
Speed of the boat downstream = Speed of the boat in still water + Speed of the stream =(15 + x) km/h
We know that
`Time = "Distance"/"Speed"`
According to question,
Time taken for upstream journey + Time taken for the downstream journey = 4 h 30 min
`:. 30/(15 - x) + 30/(15 + x) = 4 1/2`
`=> 30[((15+x)+(15 - x))/((15+x)(15-x))]= 9/2`
`=> 30(30/(225-x^2)) = 9/2`
`=> 225 - x^2 = (30 xx 30 xx 2)/9`
`=> 225 - x^2 = 200`
`=> x^2 = 225 - 200 = 25`
`=> x = +-5`
Since speed can not be negative, therefore, x = 5.
Thus, the speed of the stream is 5 km/h
