A boat takes 4 hours to travel from a place X to Y downstream and back from Y to X upstream.If the distance from X to Y is 10.5 km, and the speed of the current is 9 km/h, then the speed of the boat in still water, in km/h is:

12

Upstream Speed = Speed of Boat – Speed of current

Downstream Speed = Speed of Boat + Speed of current

Let speed of boat be a km/hr

Speed of current = 9 km/hr

Upstream speed = (a - 9) km/h

Downstream speed = (a + 9) km/h

Distance = 10.5 km

According to the question

\(\frac{10.5}{a - 9}\) + \(\frac{10.5}{ a + 9}\)  = 4 

\(\frac{10.5[(a + 9 + x - 9)]}{ (a^2 - 81) }\)  = 4

10.5 × 2a = 4a² - 324

4a² - 10.5 × 2a - 324 = 0

2a² - 10.5a - 162 = 0

After solving quadratic equation we get a = 12