# A boat goes 12 km downstream and 26 km upstream in 8 hours.It can go 16 km upstream and 32 km downstream in the same time. Find the speed of boat in still water and the speed of current.

Let the speed of the boat upstream be X and the speed of the boat downstream be Y.

The boat goes 12 km downstream and 26 km upstream in 8 hours.

=> 12/Y + 26/X = 8

It can go 16 km upstream and 32km downstream in the same time.

=> 16/X + 32/Y = 8

12/Y + 26/X = 16/X + 32/Y

=> 20/Y = 10/X

=> 2X = Y

12/Y + 26/X = 8

=> 12/2X + 26/X = 8

=> 32 = 8X

=> X = 4

Y = 8

When the boat goes downstream the speed of the current is added to the speed of the boat in still water. When it goes upstream the speed of the current is subtracted from the speed of the boat in still water.

B - C = 8 and B + C = 4

2B = 12

=> B = 6

and C = 2

**The speed of the boat in still water is 6 km/h and the speed of the current is 2 km/h**

26 km Upstream+12 km Downstream=8

16 km Upstream+12 km Downstream=8

Upstream=x-y

Downstream=x+y

Then,26/x-y + 12/x+y

& 16/x-y + 32/x+y

Let,1/x-y=a & 1/x+y=b

So, 26a + 12b = 8 ----------------(1)x8

& 16a + 32b = 8 -----------------(2)x3

208a + 96b = 64

48a + 96b = 24

(-) (-) (-)

---------------------

160a = 40

a= 40/160 = 1/4

Substituting (a) in (2)

16(1/4)+32b=8

4+32b=8

32b = 8-4 = 4

b = 4/32 = 1/8

Since b = 1/x+y

x+y=8 -----------------(3)

& a = 1/x-y

x-y=4 ------------------(4)

Adding(3) & (4)

x+y=8

x -y=4

--------

2x = 12

x=12/2

x=6km/h

Substituting x in (3)

6+y = 8

y= 8-6

y=2km/h

The speed of the boat in still water is 6 km/h and the speed of the current is 2 km/h

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