# 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. 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. 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. 3
Solve (1/2)h + (1/3)h = 1. Here's how to do it:
• (1/2)h + (1/3)h = 1 becomes (5/6)h = 1 by adding (1/2)h and (1/3)h • Multiply each side by 6/5 to undo multiplication and isolate h. You should get 6/5, which becomes 1 1/5 hrs, or 1 hour and 12 minutes. 4. 4
The job takes 1 hour and 12 minutes working together.

## Another method

1. In 6 hours Dan would finish 3 bedrooms, working alone.
2. In 6 hours Stan would finish 2 bedrooms, working alone.
3. So in 6 hours they would finish 3 + 2 = 5 bedrooms together.
4. So in 6/5 hours they would finish 1 bedroom together.
5. 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!