The Work Problem

The Work Problem

Using the WORK BOX

The “Work Problem” usually sounds like this:

Socrates can paint a room in 2 hours, Aristotle can paint the same room in 90 minutes. How long will it take them to paint the room if they work together?

Just like the “DIRTY” [D=R*T] & the “MIXED NUTS” [Wt * $ = Cost] we can use a box to lay out this unique system of equations.

Worker	Work Rate X	Time =	Work Done
Socrates	1/2	x	x/2
Aristotle	2/3	x	2x/3

You must be able to convert the work rate from the problem into the answer’s expressed units. In this case, how many hours will it take them together.

Socrates paints at 2 hrs for the whole job, so he is 1/2 of the job per hour.

Aristotle paints at 11/2 hrs for the whole job, so he is 2/3 of the job per hour. [This takes some practice ~ but is not as ugly as it looks on first glance].

Since they are working together to complete the whole job, the problem can be expressed as:

x/2 + 2x/3 = 1; combine like terms

3x/6 + 4x/6 = 1

7x/6 = 1hr.

x = 6/7 hrs.

Check your work

6/7*1/2 + 6/7*2/3 = 3/7 + 4/7 = 1

Let’s do a few more: