Question

A boat goes 30 km upward and 44 km downwards in 10 hrs. In 13 hrs it can go 40 km upstream and 55 km downstream. Find the speed of the stream and that of the boat in still water . Please solve by elmination method only.

Answer 1

Let ,

• The speed of boat in still water be " x " km/hr
• The speed of stream be " y " km/hr

Then ,

• The speed of boat downstream = (x + y) km/hr

• The speed of boat upstream = (x - y) km/hr

According to the question ,

A boat goes 30 km upward and 44 km downwards in 10 hrs

Thus ,

(30/x - y) + (44/x + y) = 30 --- (i)

And in 13 hr , it can go 40 km upstream and 55 km downstream

Thus ,

(40/x - y) + (55/x + y) = 13 --- (ii)

Put u = 1/x - y and v = 1/x + y in given two equations , we get

30u + 44v = 10 --- (iii)

40u + 55v = 13 --- (iv)

Multiply eq (iii) by 40 And eq (iv) by 30 , we get

1200u + 1760v = 400 ---- (v)

1200u + 1650v = 390 ---- (vi)

Subtract eq (vi) from eq (v) , we get

110v = 10

v = 10/110

v = 1/11

Put the value of v = 1/11 in eq (v) , we get

1200u + 1760 × (1/11) = 400

1200u = 400 - 1760/11

1200u = (4400 - 1760)/11

1200u = 2640/11

1200u = 240

u = 240/1200

u = 1/5

Since ,

u = 1/x - y and v = 1/x + y

Thus ,

x - y = 5 --- (vii)

x + y = 11 --- (viii)

Adding eq (vii) and eq (viii) , we get

2x = 16

x = 16/2

x = 8

Put the value of x = 8 in x + y = 11 , we get

8 + y = 11

y = 3

$\therefore \sf \sf \underline{The \: speed \: of \: boat \: in \: still \: water \: is \: 8 \: km/hr \: and \: the \: speed \: of \: stream \: is \: 3 \: km/hr}$