In one hour, a boat goes 11km along the stream and 5 km against it. find the speed of the boat in still water

in one hour, a boat goes 11km along the stream and 5 km against it. find the speed of the boat in still water

To find the speed of the boat in still water, we can use the concept of relative velocity. The boat’s speed in still water is the average of its speed downstream and upstream.

Let’s denote the speed of the boat in still water as ‘b’ km/h and the speed of the stream as ‘s’ km/h.

When the boat moves downstream (along the stream), its effective speed increases by the speed of the stream. So, the speed of the boat downstream is (b + s) km/h.

When the boat moves upstream (against the stream), its effective speed decreases by the speed of the stream. So, the speed of the boat upstream is (b - s) km/h.

According to the given information, in one hour the boat goes 11 km downstream and 5 km upstream.

Using the formula: distance = speed × time, we can write the following equations:

11 = (b + s) × 1 → Equation 1
5 = (b - s) × 1 → Equation 2

We have a system of two linear equations with two variables. Let’s solve it:

From Equation 1, we can simplify it to:
b + s = 11

From Equation 2, we can simplify it to:
b - s = 5

Solving these two equations simultaneously, we can find the values of ‘b’ and ‘s’.

Adding the two equations, we get:
2b = 16

Dividing both sides by 2, we find:
b = 8

So, the speed of the boat in still water is 8 km/h.

To find the speed of the stream (s), we can substitute the value of ‘b’ into one of the equations. Let’s use Equation 1:
8 + s = 11

Subtracting 8 from both sides, we get:
s = 3

Therefore, the speed of the stream is 3 km/h.

In summary, the speed of the boat in still water is 8 km/h and the speed of the stream is 3 km/h.