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

The question is not complete, the complete question is in the form of: David 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. In Routine #2, he burns calories 38 walking. He then runs at a rate that burns 8.5 calories per minute. For what amounts of time spent running will Routine #1 burn at most as many calories as Routine #2? Use for the number of minutes spent running, and solve your inequality for .

Answer:

Let us assume that the number of minutes spent running is t minute. The equation that represents the total calories burnt for routine 1 is given as:

20 + 10.5t

While the total calories burnt for routine 2 is given as:

38 + 8.5t

Since Routine #1 burn at most as many calories as Routine #2, hence it can be represented by the inequality

20 + 10.5t < 38 + 8.5t

Solving the inequality:

10.5t - 8.5t < 38 - 20

2t < 18

t < 9 minutes

For routine 1 to burn at most as many calories as routine 2, the time spent running must be less than 9 minutes