Please help me with this inequality equation!

Question

Trey is choosing between two exercise routines

in Routine #1, he burns 24 calories walking. he then runs at a rate that burns 15.5 calories per minute.

in routine #2, he burns 47 calories walking. He then runs at a rate that burns 10.9 calories per minute.

For what amount 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

For this we need to write an inequality where routine 1 is less than routine 2. We know for routine 1, he burns a total of 24 calories walking PLUS 15.5 calories for every minute (t) spent running:

24 + 15.5t

For routine 2, he burns a total of 47 calories walking PLUS 10.9 calories per minute running:

47 + 10.9t

Now we can set up our inequality:

24 + 15.5t < 47 + 10.9t

-24 -24

15.5t < 23 + 10.9t

-10.9t -1-.9

4.6t < 23

/ 4.6 / 4.6

t < 5

So the time spent running needs to be less than 5 minutes