Proportions

[KWF]

Hello:

6 workers can build a house in 8 days working 12 hours a day.

If the number of days are reduced by 1/4 to 2 days will the number of hours need to increase by 4 so that the house can be built in 2 days--1/4 X 8 days and 4 X 12 hours?

I thank you for your reply.

 

[DrPhil]

Hello:

6 workers can build a house in 8 days working 12 hours a day.

If the number of days are reduced by 1/4 to 2 days will the number of hours need to increase by 4 so that the house can be built in 2 days--1/4 X 8 days and 4 X 12 hours?

I thank you for your reply.

Working 12 hours a day is enough! I don't think you will find many workers willing to work 48 hours per day.

Better to hire more workers!

 

[KWF]

Working 12 hours a day is enough! I don't think you will find many workers willing to work 48 hours per day.

Better to hire more workers!

It is just an example to see whether or not the mathematics make sense!

 

[JeffM]

Hello:

6 workers can build a house in 8 days working 12 hours a day.

If the number of days are reduced by 1/4 to 2 days will the number of hours need to increase by 4 so that the house can be built in 2 days--1/4 X 8 days and 4 X 12 hours?

I thank you for your reply.

Yes.

How many hours does it take to build the house:

\(\displaystyle 6\ workers * \dfrac{8\ days}{worker} * \dfrac{12\ hours}{day} = 576\ hours.\) Follow that logic?

So if I cut days per worker to 2, by a factor of one fourth, I must increase the factors of the other variables so that the product of the increased factors equals 4. As DrPhil points out I cannot increase hours per day to 48. But I could increase hours per day to 16 (an increase by a factor of 4/3) and increase the number of workers to 18 (an increase by a factor of 3). Notice that 3 * (4/3) = 4.

\(\displaystyle 18\ workers * \dfrac{2\ days}{worker} * \dfrac{16\ hours}{day} = 576\ hours.\)

 

[KWF]

Yes.

How many hours does it take to build the house:

\(\displaystyle 6\ workers * \dfrac{8\ days}{worker} * \dfrac{12\ hours}{day} = 576\ hours.\) Follow that logic?

So if I cut days per worker to 2, by a factor of one fourth, I must increase the factors of the other variables so that the product of the increased factors equals 4. As DrPhil points out I cannot increase hours per day to 48. But I could increase hours per day to 16 (an increase by a factor of 4/3) and increase the number of workers to 18 (an increase by a factor of 3). Notice that 3 * (4/3) = 4.

\(\displaystyle 18\ workers * \dfrac{2\ days}{worker} * \dfrac{16\ hours}{day} = 576\ hours.\)

Thanks for the reply and information!

So, if I understand correctly, since there are 24 hours in a day one worker cannot work more than 24 hours. (?)

 

[JeffM]

Thanks for the reply and information!

So, if I understand correctly, since there are 24 hours in a day one worker cannot work more than 24 hours. (?)

A worker can certainly work more than 24 hours but certainly cannot work more than 24 hours in a single day. There are no more hours in a single day than 24. How many spoonfuls does a spoon hold?

 

[HallsofIvy]

A worker can certainly work more than 24 hours but certainly cannot work more than 24 hours in a single day. There are no more hours in a single day than 24. How many spoonfuls does a spoon hold?

Wait, wait! I can get that! Hmmm....

 

[KWF]

Wait, wait! I can get that! Hmmm....

I give up!!!! This is crazy!

 

[DrPhil]

Thanks for the reply and information!

So, if I understand correctly, since there are 24 hours in a day one worker cannot work more than 24 hours. (?)

Can't work more than 24 hours per day. And certainly couldn't work for 24 hours for 2 days in a row - that would be 48 hours without rest, or meals..

I think you should leave the hours per day at 12, and apply your proportion to the number of workers instead. OR, as JeffM suggested, make a small increase in work-hours per day, and make up the rest by increasing number of workers.

Please don't give up!