Question

You are paid 1.2 times your normal hourly rate for each hour you work over 36 hours in a week. You work 37 hours this week and earn $578.46.

What is your normal hourly rate?

(1 point)
Hourly Rate: $

Answer 1

To find your normal hourly rate, let's denote your normal hourly rate as \( r \).

You worked 37 hours in total, with 36 of those hours being at your normal rate and the additional hour being at 1.2 times your normal rate.

The earnings can be expressed as follows:

\[
\text{Total Earnings} = (\text{Hours at normal rate}) \times (\text{Normal Rate}) + (\text{Hours at overtime rate}) \times (\text{Overtime Rate})
\]

This can be expressed mathematically as:

\[
578.46 = (36 \times r) + (1 \times 1.2r)
\]

Now, simplify this equation:

\[
578.46 = 36r + 1.2r
\]
\[
578.46 = 37.2r
\]

Next, solve for \( r \):

\[
r = \frac{578.46}{37.2}
\]

Calculating it:

\[
r \approx 15.5
\]

Thus, your normal hourly rate is approximately:

\[
\text{Hourly Rate} = \boxed{15.50}
\]