First, let's determine Olivia's hourly wage. We know that she earned $1156 for 40 hours of work. To find her hourly wage, we can divide her total earnings by the number of hours worked:
\[ \text{Olivia's hourly wage} = \frac{1156}{40} = 28.9 \]
So, Olivia earns $28.90 per hour.
Next, we need to find out how much Melanie earns per hour. The equation given for Melanie's earnings is:
\[ y = 22.2x \]
To find her hourly wage, we will observe that \( y \) is her total earnings for \( x \) hours. Thus, if we want to find her hourly wage, we can assume \( x = 1 \):
\[ y = 22.2(1) = 22.2 \]
So, Melanie earns $22.20 per hour.
Now, we need to find out how much less Melanie earns than Olivia:
\[ \text{Difference in hourly wages} = \text{Olivia's hourly wage} - \text{Melanie's hourly wage} \]
Substituting the values we found:
\[ \text{Difference in hourly wages} = 28.9 - 22.2 = 6.7 \]
Therefore, Melanie earns $6.70 less per hour than Olivia.