# How to Mathematically Find the Time It Takes to Do a Job

Do you ever wonder "How long am I going to do this job" when you are with someone doing a job? This article tells you how to find the answer using rational equations. (This article uses hours for the unit of time.)

## Steps

- 1
**Figure out the problem.**Here is a prompt: Dan and Stan are cleaning their bedroom. Dan takes 2 hours to clean up his room alone. Stan does the same job in 3 hours alone. How long will it take for them to clean up the room together? - 2
**Set up the problem Here is how to set up this problem:**- Define h = number of hours Dan and Stan are working together.
- Dan's Part + Stan's Part = One Whole Bedroom
- (1/2)h + (1/3)h = 1
- These fractions come from placing the number of hours in the denominator and placing 1 on the numerator- the 1 comes from the idea that when doing a job together, each person completes a FRACTION of the whole job.

- 3
- 4
**The job takes 1 hour and 12 minutes working together.**

## Another method

- In 6 hours Dan would finish 3 bedrooms, working alone.
- In 6 hours Stan would finish 2 bedrooms, working alone.
- So in 6 hours they would finish 3 + 2 = 5 bedrooms together.
- So in 6/5 hours they would finish 1 bedroom together.
- So the answer is 6/5 hours, or 1 hour + 12 minutes.

## Tips

- To add fractions in the form 1/m + 1/n, use the shortcut (m + n)/mn. If you don't use this method, REMEMBER TO USE THE LCD!
- Show your steps and check your work. If you get a mistake, check your work and correct any mistakes you made.
- Practice this type of problem until you get the hang of it- word problems associated with rational equations aren't easy right away!

## Warnings

- SHOW AND CHECK YOUR WORK and WATCH YOUR STEPS FOR CARELESS ERRORS. One error, and you mess up the WHOLE problem.
- Don't stress yourself out while working the problem!
- This is recreational mathematics, the model behind it is often too simple to be used in real life. For example you can't put twenty cleaners in a tiny bedroom and expect them to be ready in a few minutes.

## Article Info

Categories: School Stuff