Question

A boat takes 9hrs to travel 30km upstream and 40km downstream but it takes 12 hrs to travel 42km and 50 km downstream find the speed of the stream

Answer 1

Let speed of boat = X km/h
Speed of stream = y km/h
1st equation
30 / (x - y) + 40 / (x + y) = 9 ............... (i)

2nd equation
42 / (x - y) + 50 / (x + y) = 12 .............. (ii)

Now take 1/x-y = a and 1/x+y = b
We get
30a + 40b = 9 ....... (iii)
42a + 50b = 12 ......... (iv)

Muliply (iii) by 5 & (iv) by 4 and subtract
150a + 200b = 45
168a + 200b = 48
- - -
________________
-18a = - 3
a = 3/18
a = 1/6
But a = 1/x-y = 1/6
x - y = 6 ............ (v)
Subsitute a value in (iii)
30/6 + 40b = 9
6 + 40b = 9
40b = 3
b = 3 / 40
We know b = 1 / x + y = 3 / 40
3x + 3y = 40 ................ (vi)
Multiply (v) by 3 & subtract (vi) by (v) we get
3x - 3y = 18
3x + 3y = 40
- - -
_____________
-6y = - 12
y = 2
Therefore, the speed of the stream is 2km/h