In a $100$ meter track event, Alice runs at a constant speed and crosses the finish line $5$ seconds before Beatrice does. If it took Beatrice $25$ seconds to complete the race, how many seconds would it take Alice to run $50$ meters?
I need to find Alice's speed in meters per second, and then use it to find her time for $50$ meters. To find her speed, I can use the fact that she ran $100$ meters in $5$ seconds less than Beatrice, who took $25$ seconds. That means Alice ran $100$ meters in $25 - 5 = 20$ seconds. Her speed is then $\frac{100}{20} = 5$ meters per second. To find her time for $50$ meters, I can use the formula $t = \frac{d}{s}$, where $t$ is time, $d$ is distance, and $s$ is speed. Plugging in the values, I get $t = \frac{50}{5} = 10$ seconds. 