# Problem of the Week Problem B and Solution These Rates are Shocking

## Problem

Most provinces take into consideration the time of day when they charge for electricity usage. The rates they charge are often referred to as Time-Of-Use (TOU) rates. Using the sample TOU rates in the table below, answer the questions that follow.

TOU Price Period November 1 - April 30 Time of Day May 1 - October 31 Time of Day TOU Rate ( per kWh)
Off-Peak Hours Weekdays $$7$$ p.m. - $$7$$ a.m., anytime on weekends Weekdays $$7$$ p.m. - $$7$$ a.m., anytime on weekends $$7.4{\textcent}$$
Mid-Peak Hours Weekdays $$11$$ a.m. - $$5$$ p.m. Weekdays $$7$$ a.m. - $$11$$ a.m. and $$5$$ p.m. - $$7$$ p.m. $$10.2{\textcent}$$
On-Peak Hours Weekdays $$7$$ a.m. - $$11$$ a.m. and $$5$$ p.m. - $$7$$ p.m Weekdays $$11$$ a.m. - $$5$$ p.m. $$15.1{\textcent}$$
1. Garret’s family used $$50$$ kWh on a Saturday afternoon. What would be the charge for those $$50$$ kWh?

2. On November $$10$$, when would be the best time of day to run your clothes dryer?

3. When should you avoid using your clothes dryer in the summer?

4. What might be a better way (environmentally and financially) to dry your clothes in the summer?

5. Ramal’s family used $$1180$$ kWh hours of electricity in one month.

1. What is the maximum amount of money (in dollars) they could have paid for electricity that month?

2. What is the minimum amount of money (in dollars) they could have paid for electricity that month?

## Solution

1. The rate for any Saturday is $$7.4{\textcent}$$ per kWh, which is $$\0.074$$ per kWh. Therefore, the charge for $$50$$ kWh would be $$50 \times \0.074 = \3.70$$.

2. If November $$10$$ falls on a weekday, the best time to run the dryer would be anytime before $$7$$ a.m. or after $$7$$ p.m. If November $$10$$ falls on the weekend, you could run it anytime from Friday after $$7$$ p.m. until Monday morning before $$7$$ a.m.

3. You should avoid running your dryer from $$7$$ a.m. to $$7$$ p.m. on weekdays, but it is most expensive to run your dryer between $$11$$ a.m. and $$5$$ p.m.

4. You could hang your clothes out to dry in the summer which would have little or no cost, both environmentally and financially.

1. Ramal’s family used $$1180$$ kWh. The most they could have paid for electricity is $$\0.151$$ per kWh. Therefore, the maximum amount they could have paid for electricity that month is $$1180 \times \0.151 = \178.18$$.

2. Ramal’s family used $$1180$$ kWh. The least they could have paid for electricity is $$\0.074$$ per kWh. Therefore, the minimum amount they could have paid for electricity that month is $$1180 \times \0.074 = \87.32$$.