Final answer:
To outrun the chaser with a 25mph speed, one must calculate the time the chaser takes to cover 120 yards and make sure their average velocity allows them to cover 100 yards plus 3 seconds of securing time in less time than the chaser.
Step-by-step explanation:
The objective is to find the minimum average velocity you must run to reach the destination before the person chasing you while having a 20yd head start and the person chasing you moving at an average velocity of 25mph. First, convert all units to the same system. Since velocity is given in miles per hour (mph), let's work with imperial units.
The chaser covers the 100yd distance to the destination at 25mph, which is 25 * 1760 * 3 ft/hr (since 1 mile = 1760 yards and 1 yard = 3 feet). To convert to feet per second, divide by 3600 (number of seconds in an hour). So, the chaser's speed in feet per second (fps) is (25 * 1760 * 3) / 3600. Now, calculate the time it would take the chaser to cover the 100 yards. Since you have a 20yd head start, the chaser has to cover 120 yards which in feet is 120 * 3. The time for chaser is distance/speed. We also have to add 3 seconds to your time since it takes 3 seconds to secure your position at your destination.
To win the race, your time must be less than the chaser's time. So, your total distance in feet is 100 * 3 and you have to cover it in less time than the chaser covers 120 * 3 feet. So, your speed in fps should be your total distance divided by the maximum time you have, which is the chaser's time minus 3 seconds. Finally, convert your speed back to mph by multiplying by 3600 and dividing by 5280 (since 1 mile = 5280 feet).
Remember to verify whether the obtained velocity is reasonable. As an Olympic-quality sprinter can run 100 m in roughly 10 s, which is approximately 10 m/s or about 22 mph, a speed much above this would not be reasonable for a sustained run. Therefore, if your calculated speed is much greater than that, you may want to check your conversions and calculations.