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Question 919280: 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 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 Michael to finish the job?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! lawn to be mowed is 2000 square meters.
michael can mow 1200 square meters in 8 hours.
his rate of mowing is therefore 1200 / 8 = 150 square meters per hour.
matthew can mow 600 square meters in 8 hours.
his rate of mowing is therefore = 600 / 8 = 75 square meters per hour.
mark can mow 200 square meters in 8 hours.
his rate of mowing is therefore = 200 / 8 = 25 square meters per hour.
when they work together, their rates are additive.
since rate * time = quantity, then you get:
(150 + 75 + 25) * time = 2000 square meters.
simplify by combining like terms to get:
250 * time = 2000 square meters.
divide both sides of the equation by 250 to get time = 2000 / 250 = 8 hours.
working together, they will be able to mow the the whole lawn in 8 hours.
in 5 hours, they will be able to mow 5/8 * 2000 = 1250 square meters.
looked at another way, their combined rate is 250 square meters per hour.
multiply that by 5 and you get 5 * 250 = 1250 square meters.
since the lawn is 2000 square meters and they mow 1250 square meters in 5 hours, then what is left ot mow is 750 square meters.
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