$Use first set of data to derive a second set$

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$Use first set of data to derive a second set$

a task takes 30 minutes, and yields $20 output, done with a combination of tools.
This equates to 1.1 cents/second that I am earning, for a Total $20.

One process of this task involves removing 15 screws. I time myself remove 15 screws using both a manual screwdriver, and a power driver.

I determine the power driver to be 150% more effective than the manual screwdriver method.
I.e 15 screws took 120 seconds to remove manually, or 80 seconds to remove via power driver.

My ultimate goal in doing so is to account for how much time in seconds I am saving my using the better tool, converting that time into an equivalent monetary unit, and deciding when the tool has paid for itself.

So using the sample data obtained from above:

If i determine ive unscrewed 500 screws in the past month, using a power drill method, which ive determined is 150% faster than manual, and estimate 5 seconds each screw. this is 2500 seconds ive engaged in unscrewing screws in the month.
(Using the base-line rate gained from the last known data, for ease and simplicity i.e 1.1 cents/second)

how many seconds did I save by using the drill method opposed to manual? and how much money does this equate to?

A more in-depth discussion around the problem is here:
https://www.freemathhelp.com/forum/threads/quantifing-time.135187/#post-573300

Algebra Real Analysis Word Problem

Zeanah

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There are hidden assumptions in your analysis that I will try to disentangle.

1. You did not save time per se. From your writing, it looks like you would have worked the same amount of hours regardless of the method used to unscrew the screws.

2. You are more efficient using the drill. It takes 1.5 times more time to unscrew by hand compared to unscrewing with the tool. This is based on your calculations (80 seconds with tool, 120 without it).

3. It takes 5 seconds to unscrew a screw with the tool. If you did it manually, it would take you 1.5 times more time. That means without the tool, it should take you 7.5 seconds to unscrew a screw.

4. 2500 seconds working (unscrewing with the tool) translate into 500 screws. If you didn't use the tool, those 2500 seconds would translate into 2500 secs/(7.5 secs/screw) = 333.333 screws

Using the tool allows you to unscrew 167 more screws in 2500 seconds of working (time worked is fixed).

5. This does not have to translate, necessarily, to a larger revenue. Being more efficient at one part of your job does not mean that you get paid more if you are paid to work a fixed amount of hours or your output is capped by other constraints.

For example, if you make 10 pairs of shoes a day, and find a way to make left shoes faster, but you still can only make 10 right shoes per day, you are still capped to the revenue that corresponds to 10 pair of shoes a day.

It is not explicit in your writing that the efficiency gained unscrewing gets translated into more units of your final output.

Do you get more revenue by unscrewing faster?

6. Alternatively, we can compare how much time you would need to work by hand to achieve the same number of unscrewed crews that you would get in a normal day with the tool (500 screws).

500 screws * (7.5 secs/screw) = 3750 secs

It would take you 1750 more secs to unscrew by hand and achieve the same 500 unscrewed crews (output of screws fixed)

7. Assuming there are no constraints in your output, and assuming your yield is directly proportional to the number of screws you unscrew, we can translate this time saved into money using your stated rate of 1.1 cents/second.

1750 secs * (1.1 cents/second) = $32 dollars (for every 500 screws)

But this is only true if the time freed by using the tool actually translates into getting paid at a rate of 1.1 cents/second.

If you have any questions, feel free to ask.

Mathe

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Zeanah

0

19.25 for every 500 screws, right? 1750 * 1.1 = 1925. However, I think the method of arriving was more simply executed than my brain was allowing to see, so I consider it answered. Thanks

$Use first set of data to derive a second set$

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