Step 1 :First, we need to calculate how much Raymond earned from the library by multiplying the hours he worked there by the hourly rate. This is done by the calculation \(12.5 \times 13 = 162.5\).
Step 2 :Next, we subtract this amount from the total earnings to find out how much he earned from the café. This is done by the calculation \(459.75 - 162.5 = 297.25\).
Step 3 :Finally, we divide the earnings from the café by the hours he worked there to find out the hourly rate at the café. This is done by the calculation \(297.25 \div 20.5 = 14.5\).
Step 4 :So, the café paid Raymond \(\boxed{14.5}\) per hour.