Fill Tank in 24 mins Using Pipe A & B

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In summary, the question is asking for the time it takes for Pipe A to fill the tank alone if Pipe B is closed. To find this, we first create a chart for the rates, time, and jobs for Pipe A, Pipe B, and both pipes together. Using this information, we can determine the rates for each pipe and combine them to find the rate when both pipes are open. From there, we can set up an equation and solve for the time it takes for Pipe A to fill the tank alone.
  • #1
santa
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There are two pipes, Pipe A and Pipe B. Pipe A filled a tank in for minutes less than B does. If both pipes are open the tank is filled in 24 minutes. Find the time A will take if B is closed
 
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  • #2
The bulk of the analysis for a solution is to fill a chart for Rate, Time, Job, for each of pipe A, pipe B, and pipes A and B together. If anyone knows how to present a chart in the forum, please tell; anyway, I developed this information, using t as time for pipe B to fill the tank:

pipe A: Rate? time=t-4 jobs=1
pipe B: Rate? time=t jobs=1
pipes A and B Together: Rate? time=24 minutes jobs=1

That information further indicates that These rate expressions use:
pipe A: Rate= 1/(t-4)
pipe B: Rate= 1/t
both pipes together: Rate=1/24

I did not finish the solution. Can you continue from there?
 
  • #3
Or: add rates. Since the question asks how long it will take A to fill the tank alone, let that be T minutes. Then A's rate is 1/T "tanks per minute". Since A fills the tank in 4 minutes less than B, B fills the tank in 4 minutes longer than A: it fills the tank in T-4 minutes and so its rate is 1/(T-4) "tanks per minute". Together, their rate is 1/T+ 1/(T-4). We are told that the pipes can, together, fill the tank in 24 minutes: their rate together is 1/24 "tanks per minute". Since that is exactly what we calculated before,
1/T+ 1/(T+ 4)=1/24. Solve that equation for T.
 

Related to Fill Tank in 24 mins Using Pipe A & B

1. How do Pipe A and B work together to fill the tank in 24 minutes?

Pipe A and B work together by filling the tank simultaneously. This means that water from both pipes is entering the tank at the same time, resulting in a faster rate of filling. Additionally, the size and flow rate of each pipe is carefully calculated to ensure that they work together efficiently.

2. Can the tank be filled in less than 24 minutes using Pipe A and B?

No, the tank cannot be filled in less than 24 minutes using Pipe A and B. This is because the 24-minute time frame is based on the flow rate and size of the pipes. Any changes to these factors would affect the time it takes to fill the tank.

3. How much water can be filled in the tank in 24 minutes using Pipe A and B?

The amount of water that can be filled in the tank in 24 minutes using Pipe A and B depends on the size and capacity of the tank, as well as the flow rate of the pipes. This information would need to be provided in order to determine the exact amount.

4. What happens if one of the pipes is clogged or damaged?

If one of the pipes is clogged or damaged, it will affect the flow rate and ultimately the time it takes to fill the tank. It is important to regularly maintain and check the pipes to ensure they are working properly and efficiently.

5. Are Pipe A and B the most efficient way to fill the tank in 24 minutes?

Pipe A and B are one of the most efficient ways to fill the tank in 24 minutes. However, there may be other methods or variations of Pipe A and B that could potentially fill the tank faster. It ultimately depends on the specific circumstances and resources available.

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