Question

A boat goes 45 km upstream and 65 km downstream in 14 hours. In 11 hours, it can go 35 km upstream
and 52 km downstream. Find the speed of the boat in still water and the speed of the stream.



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Answer 1

The speed of the boat in still water = 9 Km/hr

The speed of the stream = 4 Km/hr

Step-by-step explanation:

Given that,

45 km upstream and 65 km downstream in 14 hours

35 km upstream  and 52 km downstream in 11 hours

Let the boat's speed be x km/hr &

The speed of stream to be y km/hr

So,

The Speed of upstream = x - y km/hr

The speed of downstream = x + y km/hr

According to the question,

The first equation;

45/(x - y) + 65/(x + y) = 14 hours

The second equation;

35/(x - y) + 52/(x + y) = 11 hours

Now, Let

1/(x-y) = a    &  1/(x + y) = b

Now multiplying equation one by 7 and equation two by 9, we get;

∵ 45a + 65b = 14 * 7  

  35a + 52b  = 11 * 9

so,

315a + 455b = 98   ...(i)

315a + 468b = 99   ...(ii)

By  solving the two, we get

13b = 1

∵ b = 1/13

By putting the value of b in first equation, we get

45a + 65 * 1/13 = 14

45 a = 14 - 5

∵ a = 1/5

To find the value of x.

1/5 = 1/x-y

1/13 = 1/x+y

so,

x - y = 5

x + y = 13

By solving them, x is equal to 9.

and,

9 - y = 5

∵ y = 4

Thus, the speed of the boat in still water = 9km/hr

The speed of stream = 4km/hr

Learn more: Speed of boat

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Answer 2

Answer:

Step-by-step explanation:

speed of boat upstream = x-y

speed of boat downstream = x+y

equation:-

45/x-y + 65/x+y = 14 -(1)

35/x-y + 52/x+y = 11 -(2)

let 1/x-y = p and 1/x+y = q

therefore, 1 becomes

45p + 65q = 14

and 2 becomes

35p + 52q = 11

solve both by any of the methods (substituiton/cross -multiplication/elimination) then, equate the values to p=1/x-y and q=1/x+y, u'll get two equations, find their solution and thats ur answer :)