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Answer :
Final answer:
Person X and Y can mow the lawn together in 80 minutes by combining their individual rates of ½ lawn per hour for X and ¼ lawn per hour for Y to get a combined rate of ¾ lawn per hour. They finish the task in 80 minutes. So, the correct option is b.
Explanation:
To calculate how long it will take for person X and Y to mow the lawn together, we need to determine their combined rate of work. Person X can mow the lawn in 2 hours, which means X's rate is ½ lawn per hour. Person Y can mow the same lawn in 4 hours, so Y's rate is ¼ lawn per hour. Adding their individual rates gives us the combined rate: ½ + ¼ = ¾ lawn per hour.
To find the time it takes for both to mow one lawn together, we take the reciprocal of the combined rate. The reciprocal of ¾ is ⅔, or 4/3 hours. Now, we convert this time to minutes by multiplying 4/3 hours by 60 minutes per hour, resulting in (4/3) × 60 = 80 minutes. Therefore, X and Y working together will take 80 minutes to mow the lawn, which corresponds to option b) 80 minutes. By working simultaneously, X and Y can complete the task more efficiently than either could alone due to their combined working rate.
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