In a boat race, a person rows a boat 6 km upstream and returns to the starting point in 4 hours. If the speed of the stream is 2 km/hr, find the speed of the boat in still water.

Question: In a boat race, a person rows a boat 6 km upstream and returns to the starting point in 4 hours. If the speed of the stream is 2 km/hr, find the speed of the boat in still water.

Solution:
Let the speed of the boat in still water be B km/hr
⇒ Speed upstream = (B - 2) km/hr
⇒ Speed downstream = (B + 2) km / hr

We know that Time = Distance / Speed
⇒ 6/(B - 2) + 6/(B + 2) = 4
⇒ 6B + 12 + 6B - 12 = 4(B - 2)(B + 2)
⇒ 12B = 4(B - 2)(B + 2)
⇒ 3B = B² - 4
⇒ B² - 3B - 4 = 0
⇒ (B + 1) (B - 4) = 0
⇒ B = 4 km/hr (Speed cannot be negative)