inequality problems

Question

Yoko is choosing between two exercise routines.

In Routine #1, she burns 30 calories walking. She then runs at a rate that burns 6.75

 calories per minute.

In Routine #2, she does only running, burning 10.5 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

"Routine #1... at least as many ...as Routine #2"

30 + 6.75t ≥ 10.5t (see description)

solve for t:

30 ≥ 3.75t (subtract 6.75t from both sides retains sense of inequality)

8 ≥ t (divide by 3.75 retains sense of inequality)

6 ≤ 8 minutes (read from right to left)

NOTE: "for the number of minutes spent running" means that the minutes walking ARE NOT CONSIDERED