Can someone explain the steps to do this equation without actually solving it? Thank you :D

Brett can clean a house in 7 hours. Angelica can clean the same house in 3 hours. How long will it take them to clean the house if the work together?

Question

Can someone explain the steps to do this equation without actually solving it? Thank you :D

Brett can clean a house in 7 hours. Angelica can clean the same house in 3 hours. How long will it take them to clean the house if the work together?

kinggeorge · Answer

Suppose Brett can clean it in x hours, and Angelica can clean it in y hours. That means in hour, they've cleaned $${1\over x}+{1\over y}$$of the house. This is the same as $${x+y \over xy}$$This expression is how much of the house cleaned per hour. Flip it over, and you get hours per house.

kinggeorge · Answer

So if Brett takes 7 hours, Angelica takes 3 hours, in one hour they clean $${7+3\over 3\cdot7}={10\over21}$$of the house.

kinggeorge · Answer

Flip it over, and you get that it takes them $$21\over10$$hours to clean the house.

kinggeorge · Answer

Did this help you?

anonymous · Answer

It did, I used another method that I found and I got the same answer. Thank You!!!!

kinggeorge · Answer

You're very welcome.

anonymous · Answer

well to check assume there where 2 angelicas

it be  half of the time

anonymous · Answer

2 angelicas wil lbe done in 1.5 hours right?

anonymous · Answer

I got 1 hour and 1/10 minutes

anonymous · Answer

2.1 hours I think.