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The time taken by a boat while covering a certain distance upstream is thrice the time taken by it while covering the same distance in still water. If the upstream speed is 6 km/hr, what is the downstream speed?
- a)10 km/hr
- b)15 km/hr
- c)16 km/hr
- d)30 km/hr
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
The time taken by a boat while covering a certain distance upstream is...
Time → In still water : US = 1 : 3
Speed → In still water : US = 3 : 1
Speed → US : DS = 1 : (3 + 3 – 1) = 1 : 5
Hence, Option D is correct.
Speed → In still water : US = 3 : 1
Speed → US : DS = 1 : (3 + 3 – 1) = 1 : 5
Hence, Option D is correct.
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Community Answer
The time taken by a boat while covering a certain distance upstream is...
Given Information:
- Upstream speed = 6 km/hr
- Time taken upstream = 3 times the time taken in still water
Let's assume:
- Speed of the boat in still water = x km/hr
- Time taken in still water = t hours
Calculating Time taken upstream and downstream:
- Time taken upstream = Distance/ (x-6) (since speed upstream = x - 6)
- Time taken downstream = Distance/ (x+6) (since speed downstream = x + 6)
Given that time taken upstream = 3 times time taken in still water:
Distance/ (x-6) = 3t
Distance/ (x-6) = 3t
Distance/ (x-6) = t
3t = t
3 = 1
This is not possible as the times cannot be equal. Hence, the assumption that time taken in still water is t hours is incorrect.
Re-assuming:
Let's assume the time taken in still water = 1 hour.
Given that time taken upstream is 3 times time taken in still water:
Time taken upstream = 3 hours
Now, substituting the values:
Distance/ (x-6) = 3
Distance = 3(x-6)
Given that time taken downstream is 1 hour (time taken in still water):
Distance/ (x+6) = 1
Distance = x+6
Equating the two expressions for Distance:
3(x-6) = x+6
3x - 18 = x + 6
2x = 24
x = 12
Therefore, the downstream speed is x + 6 = 12 + 6 = 18 km/hr
Hence, the correct answer is 30 km/hr (Option D).
- Upstream speed = 6 km/hr
- Time taken upstream = 3 times the time taken in still water
Let's assume:
- Speed of the boat in still water = x km/hr
- Time taken in still water = t hours
Calculating Time taken upstream and downstream:
- Time taken upstream = Distance/ (x-6) (since speed upstream = x - 6)
- Time taken downstream = Distance/ (x+6) (since speed downstream = x + 6)
Given that time taken upstream = 3 times time taken in still water:
Distance/ (x-6) = 3t
Distance/ (x-6) = 3t
Distance/ (x-6) = t
3t = t
3 = 1
This is not possible as the times cannot be equal. Hence, the assumption that time taken in still water is t hours is incorrect.
Re-assuming:
Let's assume the time taken in still water = 1 hour.
Given that time taken upstream is 3 times time taken in still water:
Time taken upstream = 3 hours
Now, substituting the values:
Distance/ (x-6) = 3
Distance = 3(x-6)
Given that time taken downstream is 1 hour (time taken in still water):
Distance/ (x+6) = 1
Distance = x+6
Equating the two expressions for Distance:
3(x-6) = x+6
3x - 18 = x + 6
2x = 24
x = 12
Therefore, the downstream speed is x + 6 = 12 + 6 = 18 km/hr
Hence, the correct answer is 30 km/hr (Option D).
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The time taken by a boat while covering a certain distance upstream is thrice the time taken by it while covering the same distance in still water. If the upstream speed is 6 km/hr, what is the downstream speed?a)10 km/hrb)15 km/hrc)16 km/hrd)30 km/hrCorrect answer is option 'D'. Can you explain this answer?
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