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Question:
A person rowing at the rate of 5km/hour in still water,takes thrice as much time going 40km downstream. find the speed of stream. 2) A motor boat can travel 30km upstream and 28km downstream an 7hours.it can travel 21km upstream and returns in 5hours .find the speed of boat and speed of stream.
Answer:

1. Given the speed of the boat in still water = 5 km/hr

Let the speed of the stream  = x km/hr

So, the speed of the boat upstream = (5 - x)

and the speed of the boat downstream = (5 + x)

Give, the time to cover 40 km upstream = 3* time to cover 40 km downstream

=> 40/(5 - x) = (40*3)/(5 + x)

=> 40/(5 - x) = 120/(5 + x)

=> 1/(5 - x) = 3/(5 + x)

=> 3(5 - x) = 5 + x

=> 15 - 3x = 5 + x

=> 15 - 5 = 3x + x

=> 10 = 4x

=> x = 10/4

=> x = 2.5

So, the speed of stream = 2.5 km/hr

2. Let the speed of the boat in still water is x km/hr and the speed of the stream is y km/hr

So, the speed of the boat upstream = (x - y)

and the speed of the boat downstream = (x + y)

Now, according to question,

30/(x - y) + 28/(x + y) = 7 .............1

and 21/(x - y) + 21/(x + y) = 5

 => 1/(x - y) + 1/(x + y) = 5/21 ............2

=> {1/(x - y) + 1/(x + y)}*28 = (5/21)*28

=> 28/(x - y) + 28/(x + y) = 140/21

=> 28/(x - y) + 28/(x + y) = 20/3 ............3

Now, equation 3 - eqaution 1, we get

     2/(x - y) = 7 - 20/3

=> 2/(x - y) = (21 - 20)/3

=> 2/(x - y) = 1/3

=> 1/(x - y) = 1/6

=> x - y = 6 ............4

From eqaution 2, we get

      1/6 + 1/(x + y) = 5/21

=> 1/(x + y) = 5/21 - 1/6

=> 1/(x + y) = (5*2 - 7*1)/42

=> 1/(x + y) = (10 - 7)/42

=> 1/(x + y) = 3/42

=> 1/(x + y) = 1/14

=> x + y = 14 ........5

After solving equation 4 and 5, we get

x = 10, y = 4

So, the speed of the boat in still water is 10 km/hr and the speed of the stream is 4 km/hr

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