School cleaning

Mrs. Bart and Mr. Bart clean one floor of the school together in 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 take to clean this floor together if Mrs. Bart arrives 45 minutes later?
c. What is the latest Mr. Bart can start 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:

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

$$\begin{gathered} \frac{1}{8}\cdot (b-45/60)+1/(40/3)\cdot b=1 \\ 1/8\cdot (b-45/60)+1/(40/3)\cdot b=1 \\ 24b=131.25 \\ b=\frac{131.25}{24}=5.46875 \\ b=\frac{175}{32}=5.46875=5:28\text{h} \end{gathered}$$

$$\begin{gathered} \frac{1}{8}\cdot 6+1|(40/3)\cdot (6-c)=1 \\ 1/8\cdot 6+1/(40/3)\cdot (6-c)=1 \\ 1.8c=4.8 \\ c=\frac{4.8}{1.8}=2.66666667 \\ c=\frac{8}{3}\doteq 2.666667=2.66667=2:40\text{h} \end{gathered}$$

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