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A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours it can go 40 km upstream and 55 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
Upstream speed = speed of the boat - speed of the stream.
Downstream means a boat moves along the stream of water. Because of which
Downstream speed = speed of the boat + speed of the stream.
Required Formula:
 Distance=Speed×Time

Complete step-by-step answer:
Given :
Time taken for 30 km upstream and 44 km downstream is 10 hours.
Time taken for 40 km upstream and 55 km downstream is 13 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,
Upstream speed = b - s
Downstream speed = b + s
According to the question,
Time taken for 30 km upstream and 44 km downstream is 10 hours.
As we know that time = distancespeed
Time taken is the sum of time taken by upstream plus the time taken by downstream
 30b - s + 44b + s = 10 ………………..(1)
Time taken for 40 km upstream and 55 km downstream is 13 hours.
 40b - s + 55b + s = 13 …………….(2)
Solving 1 and 2 we get,
Multiply (1) with 4 and Multiply (2) with 3 we get,
 120b - s + 176b + s = 40 ……………….(3)
 120b - s + 165b + s = 39 ………………(4)
(3) – (4) ,
 11b + s = 1
 b + s = 11 ……………………..(5)
Substituting (5) in (4) we get,
 120b - s + 16511 = 39
 120b - s + 15 = 39120b - s = 39 - 15120b - s = 24b - s = 12024
   b - s = 5 …………………….(6)
Adding (5) and (6) we get,
 b + s + b - s = 11 + 52b = 16b = 162
 b = 8 …………..(7)
Substituting (7) in (6) we get,
 b - s = 58 - s = 58 - 5 = ss = 3
Therefore, speed of the boat “b” in still water is 8 kmph
Speed of the stream “s” is 3 kmph
So, the correct answer is “3 kmph”.

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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