The speed of a stream is 6 km/h. A boat can go 56 km downstream and 39 km upstream in 7 hours. What is the speed (in km/h) of the boat in still water?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 15.
Let speed of boat in still water ⇒ B km/h
Downstream speed ⇒ B + 6
Upstream speed ⇒ B – 6
Time ⇒ Distance ÷ Speed
According to the question
[56/(B + 6)] + [39/(B – 6)] = 7
⇒ 56(B – 6) + 39(B + 6) = 7(B2 – 36)
⇒ 56B – 336 + 39B + 234 = 7(B2 – 36)
⇒ 95B – 102 = 7B2 – 252
⇒ 7B2 – 95B – 150 = 0
⇒ (7B + 10)(B – 15) = 0
B = 15 km/h (speed cannot be negative)