if you walk for m minutes, the number c of calories used is proportional to the time you walk. if 30 caloris are used when you walk for 12 minutes, write an equation of variation and find the number of calories used when you walk for an hour
C ∝ t
or
C = kt, where k is a constant
for C=30 , t = 12
30 = k(12)
k = 30/12 = 5/2
C = (5/2)t
so for t=60
C = (5/2)(60) = 150
To write an equation of variation, let's use the formula:
c = k * m
Where:
c = number of calories used
m = time you walk in minutes
k = constant of variation
We are given that when you walk for 12 minutes, 30 calories are used. We can use this information to find the value of k.
Substituting the given values into the equation, we have:
30 = k * 12
To calculate k, divide both sides of the equation by 12:
k = 30 / 12
Simplifying:
k = 2.5
Now that we have the value of k, we can find the number of calories used when walking for an hour (60 minutes). Substituting this value into the equation:
c = 2.5 * 60
Calculating:
c = 150
Therefore, when you walk for an hour, you will use 150 calories.