The speed of a stream is 4 km/h. A boat can go 20 km downstream and 14 km upstream in 3 hours. What is the speed (in km/h) of the boat in still water?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 12.
Let speed in still water = x km/h
Downstream: 20 / (x + 4), Upstream: 14 / (x - 4)
Total time: 20 / (x + 4) + 14 / (x - 4) = 3
⇒20(x - 4) + 14(x + 4) = 3(x² - 16)
⇒20x - 80 + 14x + 56 = 3x² - 48
⇒34x - 24 = 3x² - 48
⇒3x² - 34x - 24 = 0
x = 12