A speedboat runs 6 km upstream in a river and comes back to the starting point…
2024
A speedboat runs 6 km upstream in a river and comes back to the starting point in 33 minutes. The stream of the river is running at 2 km/hr. What is the speed of speedboat in still water?
- A.
25 km/h
- B.
21 km/h
- C.
26 km/h
- D.
22 km/h
Attempted by 6 students.
Show answer & explanation
Correct answer: D
Answer: 22 km/h
Explanation:
Let the speed of the speedboat in still water be x km/h. Then downstream speed = x + 2 km/h and upstream speed = x - 2 km/h.
Time for 6 km upstream plus time for 6 km downstream equals 33 minutes = 33/60 hours, so:
6/(x - 2) + 6/(x + 2) = 33/60
Multiply both sides by (x^2 - 4): 6(x + 2) + 6(x - 2) = (33/60)(x^2 - 4). The left side simplifies to 12x, so:
12x = (33/60)(x^2 - 4) → multiply by 60: 720x = 33x^2 - 132
Rearrange: 33x^2 - 720x - 132 = 0. Divide by 3: 11x^2 - 240x - 44 = 0.
Factor the quadratic: (x - 22)(11x + 2) = 0, so x = 22 or x = -2/11. Reject the negative root because speed must be positive.
Therefore the required speed in still water is 22 km/h. Quick check: upstream time 6/20 = 0.30 h (18 min) and downstream time 6/24 = 0.25 h (15 min); total = 33 minutes.