Peter 13

Peter and Paul finished the first round of orders in 3 hours and 15 minutes. Peter, however, works a lot faster than Paul does; Peter is 2 and a half times as fast as Paul. For the second day of shipping orders, peter is unavailable; paul will have to do the same amount of work by themselves on the second day.
How long in hours : minutes will it take Paul to complete the same amount of work on their own?

Result

b = 11:23 hh:mm

Step-by-step explanation:

$$\begin{gathered} t=3:15=3hr15min=3+\frac{15}{60}=3.25hr=3.25 \\ a=b/2.5 \\ \frac{1}{a}+\frac{1}{b}=1/t \\ \frac{1}{b/2.5}+\frac{1}{b}=1/t \\ \frac{2.5}{b}+\frac{1}{b}=1/t \\ b=t\cdot (2.5+1)=3.25\cdot (2.5+1)=\frac{91}{8}=11.375=11:23\text{hh}:\text{mm} \\ \text{ Verifying Solution: } \\ a=b/2.5=11.375/2.5=\frac{91}{20}=4.55\text{h} \\ s=t\cdot (1/a+1/b)=3.25\cdot (1/4.55+1/11.375)=1 \end{gathered}$$

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