Question

Melissa is choosing between two exercise routines,In Routine #1, she burns 42 calories walking. She then runs at a rate that burns 14.25 calories per minute.In Routine #2, she burns 25 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 at most as many calories as Routine #27Use t for the number of minutes spent running, and solve your inequality for t.

Answer 1

Suppose in routine 1 and 2, Melissa rune for t minutes.

She burns 42 calories walking and then she runs at a rate that burns 14.25 calories per minute in rouitne 1.

So, total calories she burns in routine 1 is

$42+14.25t$

Again, in routine 2, she burns 25 calories walking and she runs at a rate that burns 18.5 calories per minute in rouitne 2.

So, total calories she burns in routine 2 is

$25+18.5t$

Accordingly,

$\begin{gathered} 42+14.25t\leq25+18.5t \\ 18.5t-14.25t\ge42-25 \\ 4.25t\ge17 \\ t\ge4 \end{gathered}$

So, Melissa should run for minimum 4 minutes