A boat covers a distance of 30 km downstream in 2 hours while it takes 6 hours…

Given: Distance = 30 km; Downstream time = 2 h; Upstream time = 6 h.

• Downstream speed = distance/time = 30/2 = 15 km/h.

• Upstream speed = distance/time = 30/6 = 5 km/h.

Let the boat speed in still water be b km/h and the current speed be c km/h.

• Equation 1: b + c = 15 (downstream speed).

• Equation 2: b - c = 5 (upstream speed).

Add the two equations: (b + c) + (b - c) = 15 + 5 => 2b = 20 => b = 10 km/h.

Answer: The speed of the boat in still water is 10 km/h.

Check:

• Downstream: b + c = 10 + 5 = 15 km/h => time = 30/15 = 2 h (matches).

• Upstream: b - c = 10 - 5 = 5 km/h => time = 30/5 = 6 h (matches).