the speed of a boat in still water is 15 km / hr . it can go 30 km upstream and return downstream to the orginal point in 4 hours and 30 minutes . find the speed of the stream .

Given -

Speed of water = 15km/hr

Distance travelled upstream and downstream = 30 km

Let, speed of stream be x km/hr

So, time taken to travel 30km upstream = 30/15-x

and, time taken to travel 30km downstream = 30/15+x

Time taken to travel 30km upstream and 30km downstream = 4 hour 30 min or 9/2 hours

So, the equation formed will be

30/15-x + 30/15+x = 9/2

=> 30(1/15-x + 1/15+x) = 9/2

=> 1/15-x + 1/15+x = 9/2*30 = 3/20

=> (15+x+15-x)/225 - x^{2} = 3/20

=> 30/225-x^{2} = 3/20

=> 225-x^{2} = 30*20/3

=> 225-x^{2} = 200

=> x^{2} = 225-200

=> x^{2} = 25

=> **x = 5**

__But, x = speed of stream__

__So, speed of the stream = 5 km/hr__

Hope this helps!!