Answer:
6 hours.
Step-by-step explanation:
Let t represent the time taken by apprentice in hours to make a set of glasses when working alone.
Part of work completed by apprentice in one hour would be [tex]\frac{1}{t}[/tex].
We have been given that a glassblower can produce a set of simple glasses in about 2 hours. So part of work completed by glassblower in one hour would be [tex]\frac{1}{2}[/tex].
While working together, the job takes about 1.5 hours. So part of work completed by both in one hour would be [tex]\frac{1}{1.5}[/tex].
Now we will equate sum of work competed by both in hour by work completed by both working together is one hour as:
[tex]\frac{1}{t}+\frac{1}{2}=\frac{1}{1.5}[/tex]
[tex]\frac{1}{t}\cdot 3t+\frac{1}{2}\cdot 3t=\frac{1}{1.5}\cdot 3t[/tex]
[tex]3+\frac{3}{2}\cdot t=\frac{3t}{1.5}[/tex]
[tex]3+1.5\cdot t=2t[/tex]
[tex]3+1.5t-1.5t=2t-1.5t[/tex]
[tex]3=0.5t[/tex]
[tex]\frac{3}{0.5}=\frac{0.5t}{0.5}[/tex]
[tex]6=t[/tex]
Therefore, it will take 6 hours for the apprentice to make a set of glasses when working alone.
