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?

d = (Vb-Vc)*T = 6km.

(Vb-4)T = 6.
Eq1: Vb*T - 4T = 6.

(Vb+Vc)*T = 10 km.
(Vb+4)*T = 10.
Eq2: Vb*T + 4T = 10.

Subtract the Eqs:
Vb*T - 4T = 6.
Vb*T + 4T = 10.
-8T = -4.
T = 0.5h.

In Eq1, replace T with 0.5h:
Vb*0.5 - 4*0.5 = 6.
0.5Vb = 8.
Vb = 16 km/h.

To find the speed of the boat in still water, we can use the concept of relative velocity. Let's assume the speed of the boat in still water is 'x' kph.

When the boat is traveling upstream, its effective speed is reduced by the speed of the current. Therefore, the boat's speed is (x - 4) kph.

When the boat is traveling downstream, its effective speed is increased by the speed of the current. Therefore, the boat's speed is (x + 4) kph.

Given that the boat travels 6km upstream in the same time it takes to travel 10km downstream, we can set up the following equation based on the concept of time and distance:

Time taken to travel upstream = Time taken to travel downstream

Distance/Speed upstream = Distance/Speed downstream

6/(x - 4) = 10/(x + 4)

To solve this equation, we can cross-multiply:

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

6x + 24 = 10x - 40

Subtract 6x from both sides:

24 = 4x - 40

Add 40 to both sides:

x = 64/4

x = 16

Therefore, the speed of the boat in still water is 16 kph.