Quadratic / Linear Equation: "In Grandpa Joes' garden is a 2000L large water tank..."

[luke_d]

Quadratic / Linear Equation: "In Grandpa Joes' garden is a 2000L large water tank..."

[FONT=&quot]"In Grandpa Joes' garden there is a 2000L large water tank. He usually fills the tank using recycled water from the roof which flows into the tank at a constant speed. But if he uses the garden tap which rate of flow is 5L/minute faster, it would take 20 minutes less. What is the rate of flow of the water into the tank using the recycled water?"

I managed to work out the answer, however it was through guessing. What is the process in working this one out?[/FONT]
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[luke_d]

Worded Problem - Not sure how to create an equation - Quadratic/Linear

[FONT=&quot]"In Grandpa Joes' garden there is a 2000L large water tank. He usually fills the tank using recycled water from the roof which flows into the tank at a constant speed. But if he uses the garden tap which rate of flow is 5L/minute faster, it would take 20 minutes less. What is the rate of flow of the water into the tank using the recycled water?"

I managed to work out the answer but through guessing and checking. If it helps the answer is 20L/minute. What is the process in working this one out? I tried random things but nothing worked.

T = time
L = litres in tank

L = t^2 -20t +5 ( This assignment is for Quadratics, so I assumed it was quadratic)

Then I figured it might be linear because the rates are constant. I have no idea how to do it.



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[ksdhart2]

Well, you're right that there's not much information in the problem, but there is enough to solve it. Let's begin by establishing some variables. We don't know how fast the recycled water system pumps water, so let's say that's r litres per minute. We also don't know how long it takes to fill the tank, so let's call that t minutes. Although we don't know the numerical value of t, we do know the capacity of the water tank, so we can create an expression for t in terms of r. Hypothetically, if r were 1 litre/minute, how many minutes would the tank take to fill? If it were two litres/minute? Five? In each of these cases, what process did you use to figure out how many minutes it would take? Can you apply that same process to the unknown r?

Now, the problem also tells us that if he uses the hose, which flows 5 litres/minute faster can fill the tank in 20 less minutes. What expression might you create to reflect "5 litres per minute faster?" What expression might you create to reflect "20 less minutes?" What do you know about these two expressions? Can you use them to create an equation, perhaps? If you do, you'll have two equations and two unknown variables, which means you can start solving the problem.

 

[stapel]

"In Grandpa Joes' garden there is a 2000L large water tank. He usually fills the tank using recycled water from the roof which flows into the tank at a constant speed. But if he uses the garden tap which rate of flow is 5L/minute faster, it would take 20 minutes less. What is the rate of flow of the water into the tank using the recycled water?"

I managed to work out the answer but through guessing and checking. If it helps the answer is 20L/minute. What is the process in working this one out? I tried random things but nothing worked.

T = time
L = litres in tank

L = t^2 -20t +5 ( This assignment is for Quadratics, so I assumed it was quadratic)

Okay; but by what reasoning did you arrive at this quadratic?

Then I figured it might be linear because the rates are constant. I have no idea how to do it.

While "work" word problems often have linear rates, they are usually not modelled by linear equations. To learn how to set up and solve this sort of exercise, try here. Once you have studied the lesson and learned the basic terms and techniques, the second reply you received should make much more sense!