 Problem of the Week

Problem B and Solution

Your Teeth, You Must Care For

Problem

Some dentists recommend that you brush your teeth twice a day for 2.5 minutes each time.
Assume for these problems that this recommendation has been followed. Also assume there are no leap years.

1. How many seconds per day of brushing are required by this recommendation?

2. For about how many hours would you brush your teeth in a year?

3. Over the past 25 years, for about how many days would this hockey player have brushed what teeth he has?

4. Yoda was about 900 years old. Regularly, his teeth he did brush. For about how many weeks would he have brushed his teeth throughout his life?  Time Conversion List: (Look these up if you don’t know them.)

 ____ seconds = 1 minute ____ days = 1 year ____ hours = 1 day ____ weeks = 1 year ____ days = 1 week

Solution

1. It is recommend that you brush for 2.5 minutes twice per day, for a total of 5 minutes per day. The recommended number of seconds per day is
5 minutes per day $$\times$$ 60 seconds per minute $$= 300$$ seconds per day.

2. The recommended number of minutes per year is
5 minutes per day $$\times$$ 365 days per year = 1825 minutes per year.
This is equal to 30 hours and 25 minutes, or 30$$\frac{5}{12}$$ hours $$\approx$$ 30.42 hours.
Alternatively, 5 minutes is equal to $$\frac{1}{12}$$ of an hour, giving
$$\frac{1}{12}$$ hours per day $$\times$$ 365 days = $$\frac{365}{12}$$ hours or $$30\frac{5}{12}$$ hours.

3. The number of hours of brushing in 25 years is equal to
$$\frac{365}{12}\text{ hours per year} \times$$ 25 years $$= \frac{9125}{12}$$ hours $$= 760\frac{5}{12}$$ $$\approx$$ 760.42 hours. This gives a total of $$\frac{9125}{12}$$ hours $$\div$$ 24 hours per day $$\approx$$ 31.7 days, slightly less than 32 days.

4. The number of hours of brushing in 900 years would be
$$\frac{365}{12}$$ hours per year $$\times$$ 900 years = $$\frac{328\,500}{12} = 27\,375$$ hours of brushing.
This gives $$27\,375$$ hours of brushing $$\div$$ 24 hours per day $$= 1140.625$$ days of brushing.
This is equal to 1140.625 days of brushing $$\div$$ 7 days per week $$\approx$$ 162.95 or almost 163 weeks of brushing.