Using algebra
Write $d$ for the distance of Emily's journey, and $t$ for the time it usually takes her. Then, in normal circumstances, her average speed is $\frac{d}{t}$.
Yesterday, her journey took $25\%$ longer than usual, meaning an increase of $0.25t$, so the time was $1.25t$. The distance was the same as usual.
Her average speed was therefore $\frac{d}{1.25t} = \frac{1}{1.25} \times \frac{d}{t} = 0.8\frac{d}{t}$. This means she travelled at $0.8$ of her usual average speed, which is a reduction of $0.2$ or $20\%$.