Question

7. It takes a middle school student's body 5 hours to metabolize 7 of the caffeine in a Shamrock Shake. There are

320 mg of caffeine per shake. Erin wakes up on St. Patty's Day and drinks 3 Shamrock Shakes at 7 a. M. By what

time will Erin's body have metabolized the caffeine to 60 mg?

Answer 1

To find the time it will take for Erin's body to metabolize the caffeine in the Shamrock Shakes to 60 mg, we can calculate the rate of metabolism and divide the remaining amount of caffeine by this rate.

Step-by-step explanation:

To calculate the time it will take for Erin's body to metabolize the caffeine in the Shamrock Shakes, we will first find the total amount of caffeine that Erin consumed.

Since each shake contains 320 mg of caffeine, and Erin drank 3 shakes, the total amount of caffeine consumed is 320 mg * 3 = 960 mg.

Next, we will calculate the rate at which Erin's body metabolizes caffeine per hour. If it takes 5 hours for 7% of the caffeine to be metabolized, then the rate of metabolism is 7% / 5 hours = 1.4% per hour.

Now, we can calculate the time it will take for the caffeine to be metabolized to 60 mg.

First, we subtract 60 mg from the total amount of caffeine consumed: 960 mg - 60 mg = 900 mg.

Then, we divide this remaining amount by the rate of metabolism: 900 mg / 1.4% = 64285.71 hours.

Since we want to find the time in hours, we can round up to the nearest whole hour.

Therefore, it will take approximately 64286 hours for Erin's body to metabolize the caffeine to 60 mg.