Math Is Fun Forum

Not Dav

Member

From: Animal kingdom

Registered: 2021-04-22

Posts: 55

Rational Functions and Equations Word Problems

You are going to paint your apartment. Your neighbor will paint the same apartment 5 hours sooner than you. Together, you would be able to paint the apartment in 6 hours. How long would it take each of you to paint the apartment?

I'm in pre-calc and I dont know how to start or solve the problem.

Thank you in advance, Not Dav

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Mathegocart

Member

Registered: 2012-04-29

Posts: 2,226

Re: Rational Functions and Equations Word Problems

Hello Not Dav,
Consider

to be the amount of time necessary for you to paint the apartment. Together, it takes 6 hours to paint the apartment.
Knowing these two facts, one can construct an equation:

.
Do you know how to solve the problem from there?

Last edited by Mathegocart (2022-03-02 16:14:52)

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Bob

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Registered: 2010-06-20

Posts: 10,143

Re: Rational Functions and Equations Word Problems

hi Not Dav

This is how I would do this:

Suppose there are P person-hours of work and that you take m hours.

Then your work rate is P/m and your neighbour's work rate is P/(m-5)

So if you add together your work rates:

The unknown P cancels out of this completely and the resulting equation is the same as  Mathegocart.

You then need to multiply by m(m-5) to clear the fractions and re-arrange to get a quadratic.

There are two 'solutions' but only one fits the problem as you cannot have a negative work rate for your neighbour.

Once you have a solution you can check that the numbers work ok in the original problem.

Bob

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