A boat running upstream takes 8 hours 48 minutes to cover a certain distance,…
2022
A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running towards downstream. Then the ratio between the speed of boat and the speed of the water current is
- A.
2 : 1
- B.
3 : 2
- C.
8 : 3
- D.
None of the above
Attempted by 1 students.
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Correct answer: C
For boat-and-stream problems, downstream speed equals the boat's speed plus the current's speed, and upstream speed equals the boat's speed minus the current's speed. For a fixed distance covered in different times, speed = distance ÷ time, so the two given times fix the two speeds.
Convert the upstream time to hours: 8 hours 48 minutes = 8 + 48/60 hours = 8 + 4/5 hours = 44/5 hours.
Let the common distance be D. Downstream speed = D / 4.
Upstream speed = D / (44/5) = 5D / 44.
Boat speed = half the sum of the two speeds: (D/4 + 5D/44) / 2. Writing D/4 as 11D/44, the sum is 16D/44, so boat speed = 8D/44 = 2D/11.
Current speed = half the difference of the two speeds: (11D/44 − 5D/44) / 2 = (6D/44) / 2 = 3D/44.
Boat speed : current speed = (2D/11) : (3D/44) = (8D/44) : (3D/44) = 8 : 3.
Check: with boat speed = 8k and current speed = 3k, downstream speed = 11k and upstream speed = 5k, so the time ratio (upstream : downstream) = 1/5k : 1/11k = 11 : 5 = 8.8 hours : 4 hours — exactly the 8 hours 48 minutes and 4 hours given in the question, confirming the ratio.