#### 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