Answer :
Final answer:
By taking into account the rates at which pipe A and pipe B fill the tank and the time at which each pipe starts operating, we can calculate that the tank will be filled at 11:45 a.m.
Explanation:
To calculate the time it will take for a tank to be filled by two pipes with different filling rates, we first need to find out the rate at which each pipe fills the tank and then combine these rates when both pipes are open. Pipe A fills the tank in 2 hours, and Pipe B in 6 hours.
Let's denote the capacity of the tank as 1 full tank (no units given). Therefore, the rate of Pipe A is ½ tank per hour and the rate of Pipe B is ⅓ tank per hour. When Pipe A starts at 10 a.m., by 11 a.m. it has filled ½ of the tank. At that point, Pipe B also starts filling the tank.
From 11 a.m. onwards, both pipes are working together at a combined rate of ½ + ⅓ = ⅖ tank per hour. To fill the remaining ½ tank at this rate, we calculate the time required using:
Time = Remaining Volume / Combined Rate = ½ / ⅖ = ¾ hours or 45 minutes.
Adding these 45 minutes to 11 a.m., we find that the tank will be completely filled at 11:45 a.m.
