Final answer:
By setting up an equation based on their speeds and the initial distance gap, we calculate that the total distance from Jonathan's home to the school is 2.5 miles.
Step-by-step explanation:
To solve the problem of how far the school is from Jonathan's home, we need to set up an equation to calculate the distance from the time his mother started chasing him until she caught up with him at the school entrance. Given that Jonathan was biking at 15 mph and his mother was driving at 25 mph, we can use the relative speeds to figure out how long it took for Jonathan's mother to catch up to him.
Since his mother started chasing when Jonathan was already 1 mile away from home, this initial gap needs to be closed by his mother, who travels at 10 mph faster than Jonathan (25 mph - 15 mph = 10 mph). Therefore, it would take his mother 1/10 hour, or 6 minutes, to close the 1-mile gap. During these 6 minutes, Jonathan would have traveled 1.5 miles (15 mph * 1/10 hour = 1.5 miles). So, the total distance from Jonathan's home to the school is the 1 mile plus the 1.5 miles he traveled in that time, equating to 2.5 miles.