SOLUTION: 41. Mr. Agbuya can mow a lawn in 3 hours. His sons, Michael and Ariel, can each do the job in 2 hours. If the father and the sons work together, how long would it take them to mow

Algebra ->  Rate-of-work-word-problems -> SOLUTION: 41. Mr. Agbuya can mow a lawn in 3 hours. His sons, Michael and Ariel, can each do the job in 2 hours. If the father and the sons work together, how long would it take them to mow       Log On


   

Question 927834: 41. Mr. Agbuya can mow a lawn in 3 hours. His sons, Michael and Ariel, can each do the job in 2 hours. If the father and the sons work together, how long would it take them to mow the lawn?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Mr. Agbuya can mow a lawn in 3 hours.
So Mr. Agbuya's mowing rate is 1 lawn per 3 hours or +matrix%281%2C2%2C1%2Clawn%29%2Fmatrix%281%2C2%2C3%2Chr%29+ or matrix%281%2C2%2C+1%2F3%2Clawn%2Fhr%29

His sons, Michael and Ariel, can each do the job in 2 hours.
So each of thir mowing rates is 1 lawn per 2 hours or +matrix%281%2C2%2C1%2Clawn%29%2Fmatrix%281%2C2%2C2%2Chr%29+ or matrix%281%2C2%2C+1%2F2%2Clawn%2Fhr%29

If the father and the sons work together, how long would it take them to mow the lawn?
Let the answer by x hours.

Then their combined mowing rate is 1 lawn per x hours or +matrix%281%2C2%2C1%2Clawn%29%2Fmatrix%281%2C2%2Cx%2Chr%29+ or matrix%281%2C2%2C+1%2Fx%2Clawn%2Fhr%29

The equation comes from

%28matrix%284%2C1%2C%0D%0A%22Mr.%22%2C+%22Agbuya%27s%22%2C+mowing%2C+rate%29%29%22%22%2B%22%22%28matrix%283%2C1%2C%0D%0A%22Michael%27s%22%2C+mowing%2C+rate%29%29%22%22%2B%22%22%28matrix%283%2C1%2C%0D%0A%22Ariel%27s%22%2C+mowing%2C+rate%29%29%22%22=%22%22%28matrix%284%2C1%2C%0D%0ATheir%2C+combined%2C+mowing%2C+rate%29%29


1%2F3%22%22%2B%22%221%2F2%22%22%2B%22%221%2F2%22%22=%22%221%2Fx

Clear of fractions by multiplying through by LCD of 6x.

Solve and get 3%2F4 hour.  So the can mow the lawn is 45 minutes.

Edwin