Problem Solving

Today's lesson with Brian was mostly preparing for his EOC (End Of Course) exam. Word problems often trip people up, but not because they are hard; because they have lots of words. The secret to quickly solving a word problem is to identify the math: What are the operations? What is given? What is unknown? What is the problem asking?

Example:

You burn 20 calories per minute running and 10 calories per minute swimming. Your total workout is 40 minutes of running and swimming where r is the total minutes spent running. How many calories do you burn in your 40 minute workout if you spend 20 minutes running?

The first issue here is that there are two unknowns: time spent running, r, and time spent swimming. However, since we know the total time of the workout we can put time spent swimming in terms of time spent running. Time spent swimming is the total time minus the time spent running: So time spent swimming is (40-r).

Lets build an equation: y = 20r + 10(40-r). Here we have the number of minutes spent swimming in terms of the difference between the total work out and time spent running. Each coefficient is the number of calories burned per minute for running and swimming respectively.

Now lets substitute the given information into the equation. From the last line of the word problem we know that r = 20. So we have: y = 20(20) + 10(40-20).

Easy to evaluate: y = 400 + 10(20) = 400 + 200 = 600.

So you would burn 600 calories on your 40 minute workout.

-mike-