Solve Time for Tank Filling with 2 Pipes

In summary, the problem involves filling a tank using two pipes and finding the time it takes for each pipe to fill the tank alone. Using the equation (2a+5)/a(a+5) = 1/6, which simplifies to the quadratic a^2 – 7a -30 = 0, the time for each pipe can be solved for using the quadratic formula.
  • #1
pat666
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0

Homework Statement



"A tank can be filled in 6 hours using 2 pipes. The larger pipe alone would fill it 5 hours sooner than the smaller pipe alone. How long would each pipe alone take?"

Homework Equations



I know it involves a quadratic not sure on the rest... I can't see how to do with a quadratic i mean.

The Attempt at a Solution


assume a is the big pipe and b is the small
A+B=6
A=B+5 solved them to get a=11/2hours and b=1/2, i can see that's not right. i said that a was the bigger one and my answer says that its not?
 
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  • #2
pat666 said:

Homework Statement



"A tank can be filled in 6 hours using 2 pipes. The larger pipe alone would fill it 5 hours sooner than the smaller pipe alone. How long would each pipe alone take?"

Homework Equations



I know it involves a quadratic not sure on the rest... I can't see how to do with a quadratic i mean.

The Attempt at a Solution


assume a is the big pipe and b is the small
A+B=6
A=B+5 solved them to get a=11/2hours and b=1/2, i can see that's not right. i said that a was the bigger one and my answer says that its not?


This website may help you

http://www.algebra.com/algebra/home...ems/HOW-TO-Solve-Rate-of-Work-Problems.lesson


So using the the equation form the website you get

1/a + 1/a+5 = 1/6

This simplifies to

(2a+5)/a(a+5) = 1/6

which simplifies down to the quadratic a^2 – 7a -30 = 0
 
  • #3
ok thanks
 

What is the formula for solving the time it takes to fill a tank with 2 pipes?

The formula for solving the time it takes to fill a tank with 2 pipes is T = V / (P1 + P2), where T represents the time in hours, V represents the volume of the tank in cubic meters, and P1 and P2 represent the flow rates of the two pipes in cubic meters per hour.

How do you calculate the flow rate of a pipe?

The flow rate of a pipe can be calculated by dividing the volume of water that passes through the pipe in a given time by the time taken. For example, if a pipe carries 100 cubic meters of water in 2 hours, the flow rate would be 50 cubic meters per hour.

What is the unit of measurement for flow rate?

The unit of measurement for flow rate is cubic meters per hour (m3/hr).

Can you use this formula to solve for the time it takes to fill a tank with more than 2 pipes?

Yes, this formula can be used to solve for the time it takes to fill a tank with any number of pipes. Simply add the flow rates of all the pipes together in the denominator of the formula.

How accurate is this formula for calculating the time to fill a tank?

This formula is accurate as long as the flow rates of the pipes remain constant throughout the filling process. Any changes in flow rate or other factors such as leaks or blockages may affect the accuracy of the calculation.

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