Problems with Work/Rate questions

Work Rate problems are based on two and only two concepts:
1. Rates are additive.
2. Work done = Rate * Time (much like Distance = Speed * Time)


(Remember, Rate of work is just the speed of doing work)

If I paint half a wall in an hour and if you paint half a wall in an hour, if we both work together on a wall, we will finish the wall in an hour.
If my rate of work is 1/2 wall/hour and yours is 1/2 wall/hour, our total rate of work is 1/2 + 1/2 = 1 wall/hour (that is what we mean by 'rates are additive')

Now, if the question is: How many walls will we paint together in 8 hours?

Work = Rate*Time
Work = 1*8 = 8 walls

Use these two concepts and you will be able to solve most questions.

The basic questions of work rate are of the following form:
If A, working independently, completes a job in 10 hours and B, working independently, completes a job in 5 hours, how long will they take to complete the same job if they are working together?

Since A completes a job in 10 hours, his rate of work is 1/10th of the job per hour. B's rate of work is 1/5th of the job per hour.
Their combined rate of work would then be 1/10 + 1/5 = 3/10th of the job per hour.
As we said before, Work done = Rate * Time
1 = 3/10 * T (because 1 job has to be done)
or T = 10/3 hours.
This implies that A and B will together take 3.33 hours to do the job.
Note: Time taken when A and B work together will obviously be less than time taken by A or B when they are working independently.
Note: Time is not additive. In the question above, you obviously cannot say that A and B will together take 10+5 = 15 hrs to complete the job. Working together, they will take less time than either one of them working alone takes.

Try using these two concepts to solve your work-rate problems... Post specific questions if issues arise...