Question

Ahmad is choosing between two exercise routines. In routine #1, he burns 25 calories walking. He then runs at a rate that burns 8.5 calories per minute. In routine #2, he burns 47 calories walking. He then runs at a rate that burns 5.75 calories per minute. For what amounts of time spent running will routine #1 burn fewer calories then routine #2? Use t for the number of minutes spent running, and solve your inequality for t.

Answer 1

We have

Routine #1

25 calories walking

8.5 calories per minute running

The equation of burn calories

$25+8.5t$

Routine#2

47 calories walking

5.75 calories per minute running

the equation of burn calories

$47+5.75t$

Therefore the inequality for what amounts of time spent running will routine #1 burn fewer calories then routine #2

$25+8.5t<47+5.75t$

then we need to solve this inequality

$\begin{gathered} 8.5t-5.75t<47-25 \\ 2.75t<22 \\ t<\frac{22}{2.75} \\ t<8 \end{gathered}$

In order to burn fewer calories with routine #1 than routine number #2, t must be less than 8 minutes