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:
Answer & explanation
Correct answer: option 3
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