
A boat goes km upstream and km downstream in hours. In hours it can go km upstream and km downstream. Then determine the speed of the stream and the speed of the boat in still water.
Answer
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Hint: Here we use the concept of Distance and speed involving Boats and streams.
Upstream means the boat moves against the stream of water. Because of which
Downstream means a boat moves along the stream of water. Because of which
Required Formula:
Complete step-by-step answer:
Given :
Time taken for km upstream and km downstream is hours.
Time taken for km upstream and km downstream is hours.
We need to determine the speed of the stream and the speed of the boat in still water.
Let “s” be the speed of the stream.
Let “b” be the speed of the boat in still water.
Therefore,
According to the question,
Time taken for km upstream and km downstream is hours.
As we know that
Time taken is the sum of time taken by upstream plus the time taken by downstream
………………..(1)
Time taken for km upstream and km downstream is hours.
…………….(2)
Solving 1 and 2 we get,
Multiply (1) with 4 and Multiply (2) with 3 we get,
……………….(3)
………………(4)
(3) – (4) ,
……………………..(5)
Substituting (5) in (4) we get,
…………………….(6)
Adding (5) and (6) we get,
…………..(7)
Substituting (7) in (6) we get,
Therefore, speed of the boat “b” in still water is
Speed of the stream “s” is
So, the correct answer is “ ”.
Note: Questions that involve the concept of Boats and streams are involved with distance and speed concepts. We need to have knowledge about the terms involved in the questions and the appropriate formulae needed to solve the questions. Assigning variables to the unknown terms and framing the equations as per the given conditions helps us to solve for the required quantity.
Upstream means the boat moves against the stream of water. Because of which
Downstream means a boat moves along the stream of water. Because of which
Required Formula:
Complete step-by-step answer:
Given :
Time taken for
Time taken for
We need to determine the speed of the stream and the speed of the boat in still water.
Let “s” be the speed of the stream.
Let “b” be the speed of the boat in still water.
Therefore,
According to the question,
Time taken for
As we know that
Time taken is the sum of time taken by upstream plus the time taken by downstream
Time taken for
Solving 1 and 2 we get,
Multiply (1) with 4 and Multiply (2) with 3 we get,
(3) – (4) ,
Substituting (5) in (4) we get,
Adding (5) and (6) we get,
Substituting (7) in (6) we get,
Therefore, speed of the boat “b” in still water is
Speed of the stream “s” is
So, the correct answer is “
Note: Questions that involve the concept of Boats and streams are involved with distance and speed concepts. We need to have knowledge about the terms involved in the questions and the appropriate formulae needed to solve the questions. Assigning variables to the unknown terms and framing the equations as per the given conditions helps us to solve for the required quantity.
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