SOLUTION: Three brothers,Michael,Matthew and Mark are tasked to mow a 2000 square meter garden. In 8 hours, Michael, the eldest, can mow 1200 square meters. Matthew can mow 600 square meters

Question 919307: Three brothers,Michael,Matthew and Mark are tasked to mow a 2000 square meter garden. In 8 hours, Michael, the eldest, can mow 1200 square meters. Matthew can mow 600 square meters and Mark, the youngest ca mow 200 square meters. If they work together for 5 hours, what part of the garden is not mowed?
Follow up question: with reference to the question above, suppose the three brothers worked together for 4 hours but Mark got tired and quit. Matthew stayed for another half-hour and quit. How long will it take to Michael finish the job?
Answer by Edwin McCravy(20065) (Show Source): You can put this solution on YOUR website!
Three brothers,Michael,Matthew and Mark are tasked to mow a 2000 square meter garden...
'
In 8 hours, Michael...can mow 1200 square meters.


So Michael's mowing rate is 1200 square meters per 8 hours or

In 8 hours...Matthew can mow 600 square meters


So Matthew's mowing rate is 600 square meters per 8 hours or

In 8 hours...Mark...can mow 200 square meters.


So Mark's mowing rate is 200 square meters per 8 hours or

If they work together for 5 hours,


Their combined mowing rate is  or  

Therefore in 5 hours they will have mowed  or

what part of the garden is not mowed?
`
...a 2000 square meter garden.


So 2000-1250 = 750 square meters are no mowed.

-------------------------------------------------

Follow up question: with reference to the question above, suppose the three brothers worked together for 4 hours...


Their combined mowing rate is   

Therefore in 4 hours they will have mowed  or

but Mark got tired and quit. Matthew stayed for another half-hour and quit.


Michael's and Matthew's combined mowing rate is  or .

Therefore in that half hour Michael and Matthew will have mowed  or 

So when Matthew quits, the number of square meters mowed is 1000+225+112.5 or
1337.5 square meters.

So there are 2000-1337.5 or 662.5 square meters unmowed.

How long will it take to Michael finish the job?


Since Michael's rate is ,
and , it will take him  or 4 hours and 25 minutes.

Edwin

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