Question

A glassblower can produce a set of simple glasses in about 2 h. When the glassblower works with an apprentice, the job takes about 1.5 h. How long would it take the apprentice to make a set of glasses when working alone?

Answer 1

6 hours.

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
`(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
`(1)/(2)`.

While working together, the job takes about 1.5 hours. So part of work completed by both in one hour would be
`(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:

`(1)/(t)+(1)/(2)=(1)/(1.5)`

`(1)/(t)\cdot 3t+(1)/(2)\cdot 3t=(1)/(1.5)\cdot 3t`

`3+(3)/(2)\cdot t=(3t)/(1.5)`

`3+1.5\cdot t=2t`

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

`3=0.5t`

`(3)/(0.5)=(0.5t)/(0.5)`

`6=t`

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