Solution:
Let t for the number of minutes spent running
In Routine #1, he burns 20 calories walking. He then runs at a rate that burns 10.5 calories per minute.
This can be represented as 20 + 10.5t
In Routine #2, he burns 46 calories walking. He then runs at a rate that burns 5.3 calories per minute.
This can be represented as 46 + 5.3t
The required inequality is
[tex]\begin{gathered} 20+10.5t<46+5.3t \\ 10.5t-5.3t+20<46+5.3t-5.3t \\ 5.2t+20<46 \\ 5.2t+20-20<46-20 \\ 5.2t<26 \\ \frac{5.2t}{5.2}<\frac{26}{5.2} \\ t<5 \end{gathered}[/tex]The answer is 5 minutes
