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

Algebra ->  Rate-of-work-word-problems -> 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      Log On


   

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) About Me  (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 

matrix%281%2C3%2C1200%2Csquare%2Cmeters%29%2Fmatrix%281%2C2%2C8%2Chours%29+%22%22=%22%22matrix%281%2C2%2C1200%2F8%2Cmatrix%281%2C2%2Csquare%2Cmeters%29%2Fhour%29%22%22=%22%22matrix%281%2C2%2C150%2Cmatrix%281%2C2%2Csquare%2Cmeters%29%2Fhour%29

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

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

matrix%281%2C3%2C600%2Csquare%2Cmeters%29%2Fmatrix%281%2C2%2C8%2Chours%29+%22%22=%22%22matrix%281%2C2%2C600%2F8%2Cmatrix%281%2C2%2Csquare%2Cmeters%29%2Fhour%29%22%22=%22%22matrix%281%2C2%2C75%2Cmatrix%281%2C2%2Csquare%2Cmeters%29%2Fhour%29

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

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

matrix%281%2C3%2C200%2Csquare%2Cmeters%29%2Fmatrix%281%2C2%2C8%2Chours%29+%22%22=%22%22matrix%281%2C2%2C200%2F8%2Cmatrix%281%2C2%2Csquare%2Cmeters%29%2Fhour%29%22%22=%22%22matrix%281%2C2%2C25%2Cmatrix%281%2C2%2Csquare%2Cmeters%29%2Fhour%29

If they work together for 5 hours,

Their combined mowing rate is 150%2B75%2B25 or matrix%281%2C2%2C250%2Cmatrix%281%2C2%2Csquare%2Cmeters%29%2Fhour%29 

Therefore in 5 hours they will have mowed 250%2A5 or matrix%281%2C3%2C1250%2Csquare%2Cmeters%29

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

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

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

Their combined mowing rate is  matrix%281%2C2%2C250%2Cmatrix%281%2C2%2Csquare%2Cmeters%29%2Fhour%29 

Therefore in 4 hours they will have mowed 250%2A4 or matrix%281%2C3%2C1000%2Csquare%2Cmeters%29

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

Michael's and Matthew's combined mowing rate is 150%2B75 or matrix%281%2C2%2C225%2Cmatrix%281%2C2%2Csquare%2Cmeters%29%2Fhour%29.

Therefore in that half hour Michael and Matthew will have mowed 225%2A%281%2F2%29 or matrix%281%2C3%2C112.5%2Csquare%2Cmeters%29

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 matrix%281%2C2%2C150%2Cmatrix%281%2C2%2Csquare%2Cmeters%29%2Fhour%29,
and TIME%22%22=%22%22PRODUCTION%2FRATE, it will take him 662.5%2F150=6625%2F1500=53%2F12=4%265%2F12 or 4 hours and 25 minutes.

Edwin