# A boat goes 30km upstream and 44km downstream in 10 hours. In 13 hours, it can go 40km upstream and 55km down-stream. Determine the speed of the stream and that of the boat in still water.

1
by lfstone3

## Answers

The Brainliest Answer!
2014-08-12T16:13:40+05:30
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) = 10Let 1/(x-y) = a
and 1/(x+y) = bIt implies 30a +44b = 10.......(i)
Similarly  40a+55b = 13........(ii)
Multiplying (i) by 4 and (ii) by 3 we get120a + 176b = 40...........(iii)
120a + 165b = 39..........(iv)Subtracting (iv) from (iii)
we get    44b = 12 Hence b = 1/11Putting b in (i) we get 30a + 4 = 10
Hence a = 1/5Now b = 1/x+y = 1/11or x+y = 11..........(v)and a = 1/x-y = 1/5or x-y = 5...........(vi)Adding (v) and (vi)
we get 2x = 16 Hence x = 8Putting x in (v) we get8+y = 11 Hence y = 3
Hence the speed of the boat = 8kmph
and speed of the stream = 3kmph