To determine how long it will take Patty and Mike to finish the floor together, we can calculate their combined work rate.
Let's denote their combined work rate as W. We find W by adding up their individual work rates:
Mike's work rate = 1 floor / 10 hours = 1/10 floors per hour
Patty's work rate = 1 floor / 8 hours = 1/8 floors per hour
Combined work rate (W) = 1/10 + 1/8 = 8/80 + 10/80 = 18/80 = 9/40 floors per hour
Thus, together, Patty and Mike can complete 9/40 floors per hour.
To calculate how long it will take them to finish the floor together, we use the formula:
Time = 1 floor / Combined work rate
Time = 1 / (9/40) = 40/9 ≈ 4.44 hours
Therefore, it will take Patty and Mike approximately 4.44 hours to finish the floor together.
Patty and Mike are installing new floors in their house. Working alone, Mike can complete the floor in 10 hours. Patty can complete the same floor in 8 hours if working alone. How long will it take them, working together, to finish the floor? Round your answer to the nearest hundredth if necessary.
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