B2. Laura went for a training ride on her bike. She covered the first $10 \%$ of the total distance in $20 \%$ of the total time of the ride. What was the ratio of her average speed over the first $10 \%$ of the distance to her average speed over the remaining $90 \%$ of the distance?
Solution
Let the distance Laura cycled be $10 x$ and let the time it took her be $5 t$. Then she cycled a distance $x$ in a time $t$, followed by a distance $9 x$ in a time $4 t$.
So Laura's average speed over the first $10 \%$ of the distance was $\frac{x}{t}$ and her average speed over the remaining $90 \%$ of the distance was $\frac{9 x}{4 t}$.
Hence the ratio of the speeds is $\frac{x}{t}: \frac{9 x}{4 t}=1: \frac{9}{4}=4: 9$.