Problem
Teresa is choosing between two exercise routines. In Routine $\# 1$, she burns 39 calories walking. She then runs at a rate that burns 13.75 calories per minute In Routine \#2, she burns 20 calories walking. She then runs at a rate that burns 18.5 calories per minute. For what amounts of time spent running will Routine \#1 burn fewer calories than Routine \#2? Use $t$ for the number of minutes spent running, and solve your inequality for $t$.
Solution
Step 1 ：Set up the inequality: \(39 + 13.75t < 20 + 18.5t\)
Step 2 ：Subtract 13.75t from both sides: \(39 < 20 + 4.75t\)
Step 3 ：Subtract 20 from both sides: \(19 < 4.75t\)
Step 4 ：Divide both sides by 4.75: \(t > 4\)
Step 5 ：\(\boxed{t > 4}\) minutes spent running, Routine #1 will burn fewer calories than Routine #2.
