High School

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Math 30

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Rob takes 5 hours longer than Genevieve to paint a room. If they work together, they can paint a room in 6 hours. How long does it take Rob to paint a room by himself?

Answer :

Final answer:

Rob takes approximately 12.5 hours to paint a room by himself when working alone.

Explanation:

This question involves the concept of working together and rates. To solve this, we can set up a simple equation based on the information given in the problem. It's known that when Rob and Genevieve work together, they can paint a room in 6 hours. This implies that they complete 1/6 of the work every hour.

Let's say that it takes 'G' hours for Genevieve to paint a room by herself, this means she does 1/G of the work every hour. And as it's given that Rob takes 5 hours longer to do the same job, he does 1/(G+5) of the work every hour.

As they are working together, their rates of work add up. So, we can write an equation for this: 1/G + 1/(G+5) = 1/6.

Solving this equation we find that Genevieve's time 'G' to paint a room by herself is approximately 7.5 hours. So, Rob, taking 5 hours longer than Genevieve, would need around 12.5 hours to paint a room by himself.

Learn more about working together and rates here:

https://brainly.com/question/33168847

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