A boat takes a total of 2 hours to cover 9 km downstream and return, given that the speed of the stream is 6 km/h. What is the speed of the boat in still water?

12 km/h

We know that,

Upstream Speed = Speed of boat – Speed of Stream

Downstream Speed = Speed of boat + Speed of Stream

Given,

Speed of stream = 6km/h

Distance = 9km

Time to comes back to the starting Point = 2 hours

Let the speed of the boat = a km/h

Speed of current = 6 km/h

Speed upstream = (a – 6) km/h

Speed downstream = (a + 6) km/h

Time upstream + Time downstream = 2 hours

\(\frac{9}{a - 6}\) + \(\frac{9}{a - 6}\)  = 2

= 9(a + 6 + x - 6) = 2(a² - 36)

= 9(2a) = 2a² - 72

= 2a² – 18a - 72 = 0

= a² – 9a - 36 = 0

= a² – 12a + 3a - 36 = 0

= a(a - 12) + 3(a- 12) = 0

= (a - 12)(a + 3) = 0

= a = 12