Let the original price of the shoes be \( x \).
Since the shoes were on sale for 25% off, Joe paid 75% of the original price. This can be expressed as:
\[ 0.75x = 45 \]
To find the original price \( x \), we can divide both sides by 0.75:
\[ x = \frac{45}{0.75} \]
Calculating that gives:
\[ x = 60 \]
So, the original price of the shoes was \( \boxed{60} \).