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The speed of a boat in still water is 10 m/sec and the speed of the stream is 6 m/sec. If the boat is moving upstream and back downstream, then what is the ratio of the time taken to cover a particular stretch of distance in upstream to down stream?
- a)1 : 4
- b)4 : 1
- c)2 : 3
- d)3 : 2
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The speed of a boat in still water is 10 m/sec and the speed of the st...
Since the distances travelled in each direction is the same, and the effective speeds are in the ratio, (10 − 6) : (10 + 6) = 1 : 4, the time taken to travel upstream and downstream would be in the ratio,
(1/ 1) : (1 / 4) = 4 : 1
Alternative method:
Distance travelled in one direction be x
Time is taken for covering the distance upstream
Time taken for covering the same distance downstream = 
Hence, the ratio of the times = x / 4 : x / 16 = 4 : 1
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Community Answer
The speed of a boat in still water is 10 m/sec and the speed of the st...
To solve the problem, let's consider the speed of the boat relative to the water in both cases: moving upstream and moving downstream.
Speed of the boat relative to the water when moving upstream:
Let's assume the speed of the boat in still water is B m/sec and the speed of the stream is S m/sec. When the boat moves upstream, it has to overcome the force of the stream, which is moving in the opposite direction. Therefore, the effective speed of the boat is reduced by the speed of the stream.
So, the speed of the boat relative to the water when moving upstream is B - S m/sec.
Speed of the boat relative to the water when moving downstream:
When the boat moves downstream, it gets an additional push from the stream, which is moving in the same direction. Therefore, the effective speed of the boat is increased by the speed of the stream.
So, the speed of the boat relative to the water when moving downstream is B + S m/sec.
Ratio of time taken to cover a particular stretch of distance in upstream to downstream:
Let's assume the distance to be covered is D meters.
Time taken to cover the distance when moving upstream:
The time taken to cover the distance when moving upstream can be calculated by dividing the distance by the effective speed of the boat, which is B - S m/sec.
Time taken to cover the distance when moving downstream:
The time taken to cover the distance when moving downstream can be calculated by dividing the distance by the effective speed of the boat, which is B + S m/sec.
Therefore, the ratio of the time taken to cover the distance in upstream to downstream can be calculated as:
(Time taken to cover the distance when moving upstream) : (Time taken to cover the distance when moving downstream)
= (D / (B - S)) : (D / (B + S))
= (B + S) / (B - S)
Substituting the values B = 10 m/sec and S = 6 m/sec, we get:
= (10 + 6) / (10 - 6)
= 16 / 4
= 4 : 1
Hence, the correct answer is option 'B' - 4 : 1.
Speed of the boat relative to the water when moving upstream:
Let's assume the speed of the boat in still water is B m/sec and the speed of the stream is S m/sec. When the boat moves upstream, it has to overcome the force of the stream, which is moving in the opposite direction. Therefore, the effective speed of the boat is reduced by the speed of the stream.
So, the speed of the boat relative to the water when moving upstream is B - S m/sec.
Speed of the boat relative to the water when moving downstream:
When the boat moves downstream, it gets an additional push from the stream, which is moving in the same direction. Therefore, the effective speed of the boat is increased by the speed of the stream.
So, the speed of the boat relative to the water when moving downstream is B + S m/sec.
Ratio of time taken to cover a particular stretch of distance in upstream to downstream:
Let's assume the distance to be covered is D meters.
Time taken to cover the distance when moving upstream:
The time taken to cover the distance when moving upstream can be calculated by dividing the distance by the effective speed of the boat, which is B - S m/sec.
Time taken to cover the distance when moving downstream:
The time taken to cover the distance when moving downstream can be calculated by dividing the distance by the effective speed of the boat, which is B + S m/sec.
Therefore, the ratio of the time taken to cover the distance in upstream to downstream can be calculated as:
(Time taken to cover the distance when moving upstream) : (Time taken to cover the distance when moving downstream)
= (D / (B - S)) : (D / (B + S))
= (B + S) / (B - S)
Substituting the values B = 10 m/sec and S = 6 m/sec, we get:
= (10 + 6) / (10 - 6)
= 16 / 4
= 4 : 1
Hence, the correct answer is option 'B' - 4 : 1.
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The speed of a boat in still water is 10 m/sec and the speed of the stream is 6 m/sec. If the boat is moving upstream and back downstream, then what is the ratio of the time taken to cover a particular stretch of distance in upstream to down stream?a)1 : 4b)4 : 1c)2 : 3d)3 : 2Correct answer is option 'B'. Can you explain this answer?
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