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?
Answer & explanation
Correct answer: option 4
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