Austin is choosing between two exercise routines. In Routine #1, he burns 20 calories walking. He then runs at a rate that burns 10.5 calories per minute.

Question

In Routine #2, he burns 38 calories walking. He then runs at a rate that burns 8.25 calories per minute. For what amounts of time spent running will Routine #1 burn at most as many calories as Routine #2? Use t for the number of minutes spent running, and solve your inequality for t .

Answer 1

You should first use equations to represent each routine.

 

Routine 1:  Calories burned = 20 + 10.5 *t

Routine 2: Calories burned = 38 + 8.25 * t

 

For routine 1 to burn at most as many calories as routine 2 means that routine 1 would burn less than or equal to as many calories as routine 2.

 

So your inequality should look like: routine 1 <= routine 2 

 

or

 

20 + 10.5 *t <= 38 + 8.25 * t

 

From there it should be quite easy to solve.