A log floating in a river took 24 hours to travel from A to B. Find the time (in hours) taken by a boat
to make a round trip journey between A and B, if its speed in still water is five times the speed of the
river.
(a) 6 (b) 4 (c) 5 (d) 10
Answers
Answer:
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Therefore the time taken by the boat to make a round trip journey between A and B is 10 hours.
Given:
Time taken for the log to travel from A to B = 24 hours
The speed of the boat in still water is 5 times the speed of the river.
To Find:
The time taken by the boat to make a round trip journey between A and B.
Solution:
The given question can be solved as shown below.
Let the speed of the water is V₁ and the speed of the boat be V₂.
Let the distance between A and B is d.
Given that,
Time taken for the log to travel from A to B = 24 hours
Then Velocity of log = Velocity of water
The velocity of water = V₁ = distance/time = d/24
The speed of the boat in still water is 5 times the speed of the river.
Then speed of the boat in still water = V₂ = 5V₁
Let us assume that when the boat travels from A to B the water is in upstream condition and vice versa when the boat travels from B to A.
When the boat travels from A to B ( upstream condition ):
⇒ Time taken to travel = T₁ = d/(V₂ - V₁) = d/(5V₁-V₁) = d/4V₁ = d/4(d/24) = 24/4 = 6
Hence Time taken by the boat to travel from A to B = T₁ = 6 hours
When the boat travels from B to A ( downstream condition ):
⇒ Time taken to travel = T₂ = d/(V₂+V₁) = d/(5V₁+V₁) = d/6V₁ = d/6(d/24) = 24/6 = 4
Hence Time taken by the boat to travel from A to B = T₂ = 4 hours
Total time taken = T₁ + T₂ = 6 + 4 = 10 hours
Therefore the time taken by the boat to make a round trip journey between A and B is 10 hours.
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