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.
A. 9.00 hours
B. 0.23 hours
C. 4.44 hours
D. 18.00 hours
To solve the problem, we can use the formula:
time = (amount of work) / (rate of work)
Let's say the entire floor is one unit of work. Then, in one hour, Mike can complete 1/10 of the floor, and Patty can complete 1/8 of the floor. Together, their combined rate of work is:
rate = 1/10 + 1/8 = 9/40
This means that working together, they can complete 9/40 of the floor in one hour. Using the formula above, we can solve for the time it takes to complete one unit of work:
time = 1 / (9/40) = 40/9 ≈ 4.44 hours
Therefore, the answer is (C) 4.44 hours, rounded to the nearest hundredth.
To determine how long it will take Patty and Mike to finish the floor when working together, we can use the formula:
1 / T_total = 1 / T_Patty + 1 / T_Mike
Where T_total is the time it takes them to finish together, T_Patty is the time it takes Patty to finish alone, and T_Mike is the time it takes Mike to finish alone.
Plugging in the given values:
1 / T_total = 1 / 8 + 1 / 10
Simplifying the equation:
1 / T_total = 10 / 80 + 8 / 80
1 / T_total = 18 / 80
To find T_total, we can flip the equation:
T_total = 80 / 18
Simplifying:
T_total = 4.44 hours
Therefore, the answer is C. 4.44 hours.