Question

A boat goes 30 km upstream and 44 km downstream in 10 hours .In 13 hours, it can go 40 km upstream and 53 km down-stream. Determine the speed of the stream and that of the boat in still water.

Answer 1

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Answer 2

Let the speed of boat be x km/hr
and the speed of stream be y km/hr

The the speed of boat downstream = (x+y) km/hr
And the speed of boat upstream = (x-y) km/hr

Now, speed = distance /time
Then, time = distance /speed

In the first case:
When boat moved 30km upstream, then time = 30/x-y
When boat moves 44km downstream, then time = 44/x+y
It is given that,
30/x-y + 44/x+y = 10 .......(i)

In the second case:
When the boat moves 40km upstream, then time = 40/x-y
When the boat moves 55km downstream, then time = 55/x+y
It is given that,
40/x-y + 55/x+y = 13 ......(ii)

Let 1/x-y = u and 1/ x+y = v ...(iii)
Substituting these value in eq. (i) & (ii)
we get,
30u + 44v = 10
Or 30u + 44v - 10 = 0

and 40u + 55v = 13
Or 40u + 55v - 13 = 0

By cross multiplication method,

u/44(-13)-55(-10) = v/40(-10)-30(-13) = 1/30(55)-44(40)

u/-22 = v/-10 = 1/-110

u=1/5, v=1/11

Putting the values of u and v in eq (iii), we get

1/x-y = 1/5 and 1/x+y = 1/11
x - y = 5 and x + y = 11

Now we have two another equations:
x - y = 5 ......(iv)
x + y = 11 ......(v)
By elimination y gets cancelled and we get
2x = 16
i.e. x = 8
Putting the value of x in eq. (iv), we get
8 - y = 5
i.e. y= 3

Hence, the speed of boat in still water is 8km/hr and the speed of the stream is 3km/hr