Question

A boat goes 30 km upstream and 44km downstream in10 hours. In 13 hours ' ...............answer briefly step bystep

Answer 1

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