Question

A boat takes 6hours to travel 8 km upstream and 32km downstream, and it takes 7hours to travel 20km upstream and 16km downstream find the speed of the boat in still water and the speed of the stream

who ever will answer first I will mark him as brainlist but it has to be right answer​

Answer 1

Step-by-step explanation:

Step-by-step explanation:Let the speed of the boat in still water be x km/hr and the speed of the stream be y km/hr.

∴ Speed of the boat upstream = (x – y) km/hr

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

We know that, Time = Distance ÷ Speed

As per the first condition,

8/(x – y) + 32/(x + y) = 6 ....... eq. no. (1)

As per the second condition,

20/(x – y) + 16/(x + y) = 7 ....... eq. no. (2)

Let 1/(x – y) = m and 1/(x + y) = n

∴ Equation No. (1) will become,

8m + 32n = 6 ...... eq. no. (3)

and Equation Number (2) will become,

20m + 16n = 7 ....... eq. no. (4)

Multiplying equation no. (4) by 2, we get

40m + 32n = 14 ...... eq. no. (5)

Subtracting equation (3) from equation (5)

40m + 32n = 14

8m + 32n = 6

(-) (-) (-)

32m = 8

∴ m = 8/32

∴ m = ¼

Substituting m = ¼ in equation number (3)

∴ 8m + 32n = 6

∴ 8(¼) + 32n = 6

∴ 2 + 32n = 6

∴ 32n = 6 – 2

∴ 32n = 4

∴ n = 4/32

∴ n = 1/8

Resubstituting the values of m and n we get,

m = 1/(x – y)

∴ ¼ = 1/(x – y)

∴ x – y = 4...... eq. no. (A)

n = 1/(x + y)

∴ 1/8 = 1/(x + y)

∴ x + y = 8 ....... eq. no. (B)

Adding equations (A) and (B) ,

x – y = 4

x + y = 8

2x = 12

∴ x = 12/2

∴ x = 6

Substituting x = 6 in equation (B),

∴ x + y = 8

∴ 6 + y = 8

∴ y = 8 – 6

∴ y = 2

∴ The speed of boat in still water is 6 km/hr and speed of stream is 2 km/ hr.

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Answer 2

A boat takes 6hours to travel 8 km upstream and 32km downstream, and it takes 7hours to travel 20km upstream and 16km downstream find the speed of the boat in still water and the speed of the stream