The speed of a stream is 9 km/h. A boat can cover a distance of 56 km downstream and 28 km upstream in 7 hours. Find the speed of the boat in still water (in km/h)
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 15.
Let speed of boat in still water = x km/h
Downstream speed = x + 9
Upstream speed = x - 9
Time = 56 / (x + 9) + 28 / (x - 9) = 7
Multiply through by (x + 9)(x - 9):
56(x - 9) + 28(x + 9) = 7(x² - 81)
56x - 504 + 28x + 252 = 7x² - 567
84x - 252 = 7x² - 567
7x² - 84x - 315 = 0
x² - 12x - 45 = 0
(x - 15)(x + 3) = 0
x = 15 or -3 → speed can't be negative