In the dairy 2

In a dairy they have two lines for filling milk cartons. The more modern line is one and a half times faster than the old line. When both lines work simultaneously, they fill the usual daily amount of milk cartons 5 hours earlier than when only the old line was working. Calculate in what time they fill the usual daily amount of milk cartons if only
a) the old line works b) only the new line c) both lines simultaneously.

Final Answer:

a =  8.3333 h
b =  5.5556 h
c =  3.3333 h

Step-by-step explanation:

$$\begin{gathered} b=a/1.5 \\ (a-5)\cdot (1/a+1/b)=1 \\ (a-5)\cdot (1/a+1/(a/1.5))=1 \\ (a-5)\cdot (1+1.5)=a \\ 1.5a=12.5 \\ a=\frac{12.5}{1.5}=8.33333333 \\ a=\frac{25}{3}\doteq 8.333333=8.3333\text{h} \end{gathered}$$

$b=a/1.5=8.3333/1.5=5.5556\text{h}$

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