# 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 down- stream. Determine the speed and that pf the boat in still water....????kindly explain this question....

• 3

Let the speed of boat in still water be 'x' km/h and speed of still water be 'y' km/h

Now, Speed in downstream= (x+y)km/h

Speed in upstream= (x-y)km/h

Now, According to given question,

30/x-y + 44/x+y= 10 ---(1)

40/x-y + 55/x+y= 13---(2)

Let 1/x-y be 'u' and 1/x+y be 'v'

So 30u+44v= 10 ----(3)

40u+55v=13 ---(4)

Multiply Equation (3) by 4 and Equation (4) by 3,

120u+176v=40 ---(5)

120u+165v=39 ---(6)

(-)      (-)       (-)    (Subtracting)

11v=1

=> v=1/11

Now, Similarly u'll get all the value of u, x and y.

Hope it helps!

• 15

gr8est ansseerrr thumps up.... aur bhi milenge aapko

• 6

Now, 30u+44v=10

=> 30u+44*1/11=10

=> 30u= 10-4

=> u= 6/30

=> u=1/5

Now, 1/x-y= u

=> 1/x-y=5

=> x-y=5

=> x= 5+y ----(7)

Now, v= 1/x+y

=> 1/11= 1/x+y

=> x+y=11 ---(8)

=> 5+y+y=11 (from 7)

=> 2y= 6

=> y= 3

Also x= 5+y

=> x= 5+3

x= 8

Therefore speed of boat is x km/h or 8km/h and speedd of still water is y km/h or 3km/h

• 31

Let the speed of the boat be x and the speed of the strean be y

Then speed of the boat in upstream = (x-y) kmph

The speed of the boat in downstream = (x+y) kmph

Then 30/(x-y) + 44/(x+y) = 10

Let 1/(x-y) = a and 1/(x+y) = b

It implies 30a +44b = 10.......(i)

Similarly 40a+55b = 13........(ii)

Multiplying (i) by 4 and (ii) by 3 we get

120a + 176b = 40...........(iii)

120a + 165b = 39..........(iv)

Subtracting (iv) from (iii) we get

11b =1 Hence b = 1/11

Putting b in (i) we get

30a + 4 = 10 Hence a = 1/5

Now b = 1/x+y = 1/11

or x+y = 11..........(v)

and a = 1/x-y = 1/5

or x-y = 5...........(vi)

Adding (v) and (vi) we get

2x = 16 Hence x = 8

Putting x in (v) we get

8+y = 11 Hence y = 3

Hence the speed of the boat = 8kmph

and speed of the stream = 3kmph