Question

a boat goes 12 km upstream and 40 dwnstrm...in 8 hrs. it can go 16 km upstrm and 32 km dwnstrm in same time.....find the apead of boat in still water and spead of stream

Answer 1

Let the speed of boat be 'x' && speed of stream be 'y'
Down stream speed = x+y
Upstream speed = x-y
Given,
12/x-y + 40/x+y = 8
divide R.H.S and L.H.S by '4'
3/x-y + 10/x+y = 2....(i)

16/x-y + 32/x+y = 8
Divide R.H.S and L.H.S by '8'
2/x-y + 4/x+y = 1....(ii)

eq. (i) x 2    &&   eq. (ii) x 3
6/x-y + 20/x+y = 4......(iii)
6/x-y + 12/x+y = 3......(iv)
(iii) - (iv)
20/x+y - 12/x+y = 4-3 = 1
8/x+y = 1
x+y = 8.....(a)
(a) in (ii)
2/x-y + 4/8 = 1
2/x-y = 1 - 1/2 = 1/2
x-y = 4....(b)
(a) + (b)
2x = 12
x = 6.... y = 2
Speed of boat = 6 km/hr
Speed of stream = 2 km/hr
Hope it helps.

Answer 2

Let the speed of the boat in still water be x km/hr.

Let the speed of the stream be y km/hr.

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

The speed of the boat downstream  =x+y

Since

Therefore,

and,

Suppose,

So, the equations become 8 = 12p + 40q

               and  8 = 16p + 32q

Now, solve the equations for p and q by elimination method and replace p by x-yand q by x+y.

You get, x-y = 4

     x+y = 8

Solve these equations for x and y by elimination method. So, the speed of the boat in still water is 6 km/hr. and the speed of the stream is 2 km/hr.