Question

Ravi is choosing between two exercise routines.In Routine #1, he burns 20 calories walking. He then runs at a rate that burns 18.5 calories per minute.In Routine #2, he burns 46 calories walking. He then runs at a rate that burns 13.3 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.

Answer 1

The amount of calories burnt in t mins in Routine #1 is given by:

$20+18.5t$

The amount of calories burnt in t mins in Routine #2 is given by:

$46+13.3t$

For the time period when the amounts of time spent running in Routine #1 burn fewer calories than Routine #2, we have:

$\begin{gathered} 20+18.5t\lt46+13.3t \\ \text{ Subtract }13.3t\text{ from both sides of the equation:} \\ 20+18.5t-13.3t\lt46+13.3t-13.3t \\ 20+5.2t\lt46 \\ \text{ Subtract }20\text{ from both sides of the equation:} \\ 20-20+5.2t\lt46-20 \\ 5.2t\lt26 \\ \text{ Dividing both sides by }5.2 \\ t\lt\frac{26}{5.2}=5 \\ t\lt5 \end{gathered}$

Since t is non-negative, it follow that the solution is given by:

0 ≤ t ≤ 5

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