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. Image titled Mathematically Find the Time It Takes to Do a Job Step 1
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    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. Image titled Mathematically Find the Time It Takes to Do a Job Step 2
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    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.
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    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
      Image titled Mathematically Find the Time It Takes to Do a Job Step 3Bullet1
    • 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.
      Image titled Mathematically Find the Time It Takes to Do a Job Step 3Bullet2
  4. Image titled Mathematically Find the Time It Takes to Do a Job Step 4
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    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!
  • 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