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jeka57 [31]
3 years ago
13

A glassblower can produce a set of simple glasses in about 2 h. When the glassblower works with an apprentice, the job takes abo

ut 1.5 h. How long would it take the apprentice to make a set of glasses when working alone?
Mathematics
1 answer:
Snowcat [4.5K]3 years ago
7 0

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 \frac{1}{t}.

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 \frac{1}{2}.

While working together, the job takes about 1.5 hours. So part of work completed by both in one hour would be \frac{1}{1.5}.

Now we will equate sum of work competed by both in hour by work completed by both working together is one hour as:

\frac{1}{t}+\frac{1}{2}=\frac{1}{1.5}

\frac{1}{t}\cdot 3t+\frac{1}{2}\cdot 3t=\frac{1}{1.5}\cdot 3t

3+\frac{3}{2}\cdot t=\frac{3t}{1.5}

3+1.5\cdot t=2t

3+1.5t-1.5t=2t-1.5t

3=0.5t

\frac{3}{0.5}=\frac{0.5t}{0.5}

6=t

Therefore, it will take 6 hours for the apprentice to make a set of glasses when working alone.

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