School cleaning

Mrs. Bart cleans 1 floor of the school together for 5 hours. Mrs. Bart can clean this floor by herself in 8 hours.
a. In how many hours can Mr. Bart clean this floor by himself?
b. How long will they clean this floor together if Mrs. Bart arrives 45 minutes later?
c. What is the latest Mr. Bart can be so that the cleaning is finished in 6 hours?

Result

a = 13:20 h
b = 5:28 h
c = 2:40 h

Step-by-step explanation:

$$\begin{gathered} 5(1/8+1/a)=1 \\ a=1/(1/5-1/8)=\frac{40}{3}=13.33333=13:20\text{h} \end{gathered}$$

1/8·(b-45/60)+1/(40/3) · b = 1

24b = 131.25


b = 131.25/24 = 5.46875

b = 175/32 = 5.46875

Our simple equation calculator calculates it.

1/8·6+1/(40/3) · (6-c) = 1

1.8c = 4.8


c = 4.8/1.8 = 2.66666667

c = 8/3 ≈ 2.666667

Our simple equation calculator calculates it.

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