A boat sailing against a stream of river takes 6 hours to travel 24 kms while sailing with thestream it takes 4 hours to travel the same distance. What is the speed o fthe stream?

Let's denote the speed of the boat in still water as "b" km/hr and the speed of the stream as "s" km/hr.

When the boat is sailing against the stream, its effective speed is reduced by the speed of the stream, so it travels at (b - s) km/hr. When it's sailing with the stream, its effective speed is increased by the speed of the stream, so it travels at (b + s) km/hr.

Given the following information:

When sailing against the stream, it takes 6 hours to travel 24 km. This can be expressed as: Distance = Speed × Time 24 km = (b - s) × 6 hours

When sailing with the stream, it takes 4 hours to travel the same distance: 24 km = (b + s) × 4 hours

Now, let's solve this system of linear equations:

From the first equation, we can express (b - s) as: b - s = 24 km / 6 hours = 4 km/hr

From the second equation, we can express (b + s) as: b + s = 24 km / 4 hours = 6 km/hr

Now, we have a system of two equations:

1. b - s = 4
2. b + s = 6

We can solve this system by adding the two equations:

(b - s) + (b + s) = 4 + 6 2b = 10

Now, divide both sides by 2 to find the speed of the boat in still water (b):

b = 10 / 2 = 5 km/hr

Now that we know the speed of the boat in still water (b), we can find the speed of the stream (s) using either of the two equations:

b - s = 4

5 km/hr - s = 4

Subtract 4 from both sides:

-s = 4 - 5

-s = -1

Now, multiply both sides by -1 to solve for s:

s = 1 km/hr

So, the speed of the stream is 1 km/hr.