Earlier I blogged about rate problems involving distance. This post is about rate problems involving work! I find that one of the reasons that work-related rate problems are so difficult is because rate problems not only tend to be a bit unrealistic, they also conjure up some incredibly boring and strange tasks! Some common work-related problems are how long it takes to mow an area of lawn, to paint a number of houses, etc.
Let’s look at an example that will hopefully be slightly more exciting (as exciting as rate problems are going to get) than houses getting painted and lawns being mowed. As someone studying and preparing for the GRE, let’s do a hypothetical example on how many cups of coffee a student drinks per day in the final week before test day:
This problem is slightly different than most rate problems, since we’re given the total work done (how many cups have been consumed) and the rate (the time per cup of coffee consumed) and we’re asked to find the amount of time studying.
Another word of caution for this problem is that the rate is in minutes and the final
answer asks for hours. There’s two options: to convert the rate to cups/hour or to find a
final answer in minutes and then convert to hours, either is acceptable.
My biggest piece of advice for rate problems (distance, work, or other) is to use units. So our problem gives two bits of information:
- The rate of coffee drinking 1 cup/45 minutes or we can also invert it to get 45 minutes/1 cup of coffee.
- Our mysterious academic master has had a total of 4 cups of coffee.
In the solution to this problem, we converted cups/min into cups/hour since it’s a great example of rate conversion!