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Muriel can do the laundry in 3 hours working alone. Rea has more experience and can do the laundry in 2 hours working alone. How long will it take both people to do the laundry working together?

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Here we have a problem of rates of work, where we want to find the rate at which two people would work together, so we can find the time it takes to complete a given job when these two work together..

We will find that they need to work for 6/5 hours to do the laundry together.

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We know that:

  • Muriel can do the laundry in 3 hours.
  • Rea can do the laundry in 2 hours.

Then we can define:

  • M = rate at which Muriel works = 1/3h
  • R = rate at which Rea works = 1/2h

Where the rates are computed as the quotient between 1 (1 total laundry completed) and the amount of time it takes to do it.

If they work together, the rate just adds up, so we will have:

rate = (M + R) = 1/3h + 1/2h

Now we need to write that as a single fraction, so we get:

rate =  1/3h + 1/2h = 2/6h + 3/6h = 5/6h

Now we can write an equation of the form:

rate*time = 1

Where the 1 again, means "one complete laundry done".

Then we have:

(5/6h)*T = 1

T = (6/5)h

This means that they need to work for (6/5) hours to do the laundry together.

If you want to learn more, you can read:

https://brainly.com/question/14305692

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