The speed of a stream is 9 km/h. A boat can go 28 km downstream and 20 km upstream in 8 hours. What is the speed (in km/h) of the boat in still water?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 12.
Let boat speed in still water = B km/h
Downstream speed = B + 9
Upstream speed = B − 9
28/(B + 9) + 20/(B − 9) = 8
⇒ 28B − 252 + 20B + 180 = 8(B2 − 81)
⇒ 48B − 72 = 8B2 − 648
⇒ 0 = 8B2 − 48B − 576
⇒ 0 = BB2 − 6B − 72
⇒ (B − 12)(B + 6) = 0
The speed (in km/h) of the boat in still water ⇒ B = 12 km/h