SOLUTION: what is the step by step of solving this problem?. Dan can clean the garage in 6 hours. Bea can do the same job in 8 hours.If they work together, how long will it take them to clea

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Question 173401: what is the step by step of solving this problem?. Dan can clean the garage in 6 hours. Bea can do the same job in 8 hours.If they work together, how long will it take them to clean the garage?. please help me, thank you very much.
Answer by Edwin McCravy(20086) About Me  (Show Source):
You can put this solution on YOUR website!
Dan can clean the garage in 6 hours. Bea can do the same job in 8 hours.If they work together, how long will it take them to clean the garage?. please help me, thank you very much.

Let "x hours" be the answer.

>>...Dan can clean the garage in 6 hours...<< 

Therefore in 1 hour he can clean 1%2F6th of the garage.
Therefore in the x hours he has cleaned x%2F6ths of the garage.

>>...Bea can do the same job in 8 hours...<<

Therefore in 1 hour she can clean 1%2F8th of the garage.
Therefore in the x hours she has cleaned x%2F8ths of the garage.

The two fractions of the garage each of them has cleaned must 
add up to one (1) whole garage cleaned, so

matrix%281%2C5%2Cx%2F6%2C++%22%2B%22%2C+++x%2F8%2C+%22=%22%2C+1%29

Multiply through by the LCD of 24:

matrix%281%2C5%2C24%28x%2F6%29%2C++%22%2B%22%2C+++24%28x%2F8%29%2C+%22=%22%2C+24%281%29%29

matrix%281%2C5%2C4x%2C++%22%2B%22%2C+++3x%2C+%22=%22%2C+24%29

matrix%281%2C3%2C7x%2C+%22=%22%2C+24%29

matrix%281%2C3%2Cx%2C+%22=%22%2C+24%2F7%29

matrix%281%2C4%2Cx%2C+%22=%22%2C+3%263%2F7%2C+hours%29

Edwin