3.7. Applications to Work, Fluid Flow, and Energy Flow
3.7.1. Solving Rate Problems
We already considered word problems involving constant rates when we learned about uniform motion. This will now make it easier for us to solve other problems in which the quantities are related in the same way. These are work, fluid flow, and energy flow.
|Uniform motion:||amount traveled = rate of travel × time traveled|
|Work:||amount of work done = rate of work × time worked|
|Fluid flow:||amount of flow = flow rate × duration of flow|
|Energy flow:||amount of energy = rate of energy flow × time|
Notice that these equations are mathematically identical. Many applications involving motion, flow of fluids or solids, flow of heat, electricity, solar energy, mechanical energy, and so on, can be handled in the same way.
To convince yourself of the similarity of all of these types of problems, consider the following work problem:
If worker M can do a certain job in 5 h, and N can do the same amount in 8 h, how long will it take M and N together to do that same amount?
Are the following problems really any different?
To tackle work problems, we need one simple idea.
Here we require that the rate of work is constant. We often use this equation to find the rate of work for a person or a machine.