Basic Work Problems

Work problems are just another type of Rate problem. Instead of distances, however, these questions are concerned with the amount of “work” done.

Work takes the place of distance. Instead of RT = D, use the equation RT = W. The amount of work done is often a number of jobs completed or a number of items produced.

Time is the time spent working.

Rate expresses the amount of work done in a given amount of time. Rearrange the equation to isolate the rate:

Be sure to express a rate as work per time (W/T), NOT time per work (T/W). For example, if a machine produces pencils at a constant rate of 120 pencils every 30 seconds, the rate at which the machine works is

Many Work problems will require you to calculate a rate. Try the following problem:

  1. Martha can paint of a room in hours. If Martha finishes painting the room at the same rate, how long will it have taken Martha to paint the room?

    1. hours
    2. 9 hours
    3. hours
    4. hours
    5. hours

    Your first step in this problem is to calculate the rate at which Martha paints the room. You can say that painting the entire room is completing 1 unit of work. Set up an RTW chart:

      R
    (rooms/hr)    		 × T
    (hr)    		 = W
    (rooms)
    Martha r

    Now solve for the rate:

    The division would be messy, so leave it as a fraction. Martha paints of the room every hour. Now you have what you need to answer the question. Remember, painting the whole room is the same as doing 1 unit of work. Set up another RTW chart:

      R
    (rooms/hr)    		 × T
    (hr)    		 = W
    (rooms)
    Martha
    		t
    		1

    Now solve for the time:

    The correct answer is (D). Notice that the rate and the time in this case were reciprocals of each other. This will always be true when the amount of work done is 1 unit (because reciprocals are defined as having a product of 1).