The speed of the current is 4kph. A boat travels 6km upstream in the same time it takes to travel 10km downstream. What is the spees of the boat in still water?

distance=(current+boat)*time

Upstream:
6km=(B-4)t
Downstream
10km=(b+4)t

the times are identical, so

6/(B-4)=10/(B+4) or

6(B+4)=10(B-4)
solve for B..
4B=16
B=4km/hr

To solve this problem, we need to use the concept of relative speed.

Let's assume the speed of the boat in still water is 'b' km/h. The speed of the current is given as 4 km/h.

When the boat travels upstream, its effective speed is reduced by the speed of the current. So, the effective speed upstream would be (b - 4) km/h.

When the boat travels downstream, its effective speed is boosted by the speed of the current. So, the effective speed downstream would be (b + 4) km/h.

Now, we can set up a ratio based on the given information:

Upstream Distance / Speed Upstream = Downstream Distance / Speed Downstream

6 km / (b - 4) km/h = 10 km / (b + 4) km/h

To solve this equation, we can cross-multiply:

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

6b + 24 = 10b - 40

Rearranging the equation:

10b - 6b = 24 + 40

4b = 64

Dividing both sides by 4:

b = 16

Therefore, the speed of the boat in still water is 16 km/h.