word problem question

Question

Alan is choosing between two exercise routines.

In Routine #1, he does only running, burning 18.5

 calories per minute.

In Routine #2, he burns 22

 calories walking. He then runs at a rate that burns 16.3

 calories per minute.

For what amounts of time spent running will Routine #1 burn at least as many calories as Routine #2?

Use t

 for the number of minutes spent running, and solve your inequality  for t

. 

Answer 1

It's given that t = time in minutes

For Routine #1, Calories burned amount to 18.5t

For Routine #2, Calories burned amount to 22 + 6.3t

For Calories in Routine #1 to be at least equal to the calories in Routine #2 we have the following inequality

18.5t ≥ 22 + 6.3t

Subtracting 6.3t from both sides, 18.5t-6.3t ≥ 22 + 6.3t - 6.3t

or 2.2t ≥ 22

So t ≥ 10 minutes; So Alan must run at least 10 minutes