Final answer:
By setting up equations for the distances that James and Mitch travel and equalizing them, we find that the time 't' after which they meet is 200 seconds. However, this doesn't match the provided multiple-choice options, indicating a potential error in the question or options.
Step-by-step explanation:
To determine after how long James and Mitch will meet on their way to school, we need to calculate the time it takes for both of them to cover a distance where their paths intersect considering their starting points and speeds.
Let's denote James' starting distance to school as x meters. Since Mitch's house is 100 meters further, his starting distance to school will be x + 100 meters. Now, let's set up the equations based on their speeds where t is the time in seconds after which they meet.
For James: Distance traveled = speed × time, so:
x = 2t
For Mitch: Distance traveled = speed × time, so:
x + 100 = 2.5t
Setting the two expressions for x equal to each other gives us:
2t = 2.5t - 100
Now, we solve for t:
0.5t = 100
t = 200
Therefore, the time after which they meet is 200 seconds.
However, this answer does not match any of the provided options (a) 50 seconds, (b) 40 seconds, (c) 25 seconds, (d) 20 seconds, therefore there might be a mistake in the problem statement or in the given options.