Question

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

Answer 1

Note:
time=speed/distance.

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 as per the details in 1srlt case,
30/(x-y) + 44/(x+y) = 10

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

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

Similarly as perbthe second case,
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