Answer :
Final answer:
The tank will be filled at 11:45 a.m. This is determined by calculating the combined fill rate of Pipe A and B once Pipe B is opened at 11 a.m. and considering the half-filled tank by Pipe A at that time.
Explanation:
The question is asking how long it will take to fill a tank with water using two different pipes that have different fill rates. Pipe A can fill the tank in 2 hours, while Pipe B can fill it in 6 hours.
Pipe A is opened at 10 a.m., so by 11 a.m., it has already filled half of the tank since it can fill the entire tank in 2 hours. When Pipe B is opened at 11 a.m., we need to calculate the combined filling rate of both pipes.
Let's define the rate of Pipe A as 1 tank/2 hours = 1/2 tank per hour and Pipe B as 1 tank/6 hours = 1/6 tank per hour. The combined rate is (1/2) + (1/6) = 3/6 + 1/6
= 4/6
= 2/3 tank per hour.
Since half the tank is already filled by Pipe A alone, we have 1/2 tank left to fill.
To find how long it takes both pipes to fill the remaining 1/2 tank, we divide the remaining volume by the combined rate: (1/2) / (2/3) = (1/2) * (3/2) = 3/4 hours, which is 45 minutes.
Therefore, adding 45 minutes to 11 a.m. gives us 11:45 a.m. as the time when the tank will be completely filled with both pipes open.
