Work and rate problems are very similar to speed and distance problems, because you have a rate multiplied by a unit of time, resulting in an overall accomplishment, (distance or work). Like speed and distance problems, work and rate problems won’t come in a simple form. You will need to manipulate the work equation to find your solution. The most important equation to remember is:
Unlike speed and distance problems, work can come in a plethora of forms. For example, the work may just be represented as a job or it could be digging a hole, painting a wall, building boxes, etc etc. What the job is doesn’t really matter, but its always important that the equation is represented properly and the numerators and denominators cancel each other out. For example:
Jane can build 3 boxes in an hour. She must build 9 boxes to complete a job. How long does it take her to complete a job?
We know that Jane’s rate is 3 boxes per hour, and it takes 9 boxes to complete a job, so we can figure out how long that takes by solving for the following equation.
(3 boxes/hour) (X hours) = 1 job
However we need to put the right side of the equation in the same terms as the left side of the equation, so it is actually solvable. When we do this we get:
(3 boxes/hour) (X hours) = 9 boxes
From there, we can deduce that it takes 3 hours to complete 9 boxes or 1 job.
Often times, the “work” can be arbitrary. It’s important to remember to be consistent. Also, it can be easier to write everything down into smaller equations first, so its easier to figure out how they go together.