please help with inequality word problem!

Question

Tammy is choosing between two exercise routines.
In Routine #1, she does only running, burning
12.5
calories per minute.
In Routine #2, she burns
23
calories walking. She then runs at a rate that burns
6.75
calories per minute.
For what amounts of time spent running will Routine #1 burn more calories than Routine #2?
Use
t
for the number of minutes spent running, and solve your inequality for
t

Answer 1

Hi Nina

 

So the amount of calories you burn is the rate of calories you burn per minute times the number of minutes you spend burning them.  Routine 1 is then 12.5 * t.  Routine 2 is a flat amount of calories burned of 23 + 6.75 * t and since you want to know at what value of t Routine 1 gives you more calories burned than Routine 2 so set your equation up like this:

 

12.5t > 23 + 6.75t

-6.75t          -6.75t

5.75t > 23

/5.75    /5.75

      t > 4

 

So for any workout greater than 4 minutes you will burn more calories on Routine 1

 

Hope this helps

 

Lori