One runner has run 15 miles this month and plans to run 2 1/2 miles per day for the rest of the month. Another runner has not yet run this month but plans to run 3 1/4 miles per day for the rest of the month. After how many days will the two runners have run the same number of miles?

After 20 days, the two runners will have run the same number of miles

Step-by-step explanation:

The problem can be solved by using equations. However, we'll approach the solution by using pure reasoning and logic, besides calculations.

The first runner has already run 15 miles this month and plans to run 2 1/2=2.5 miles per day for the rest of the month.

The other runner has not yet run and plans to run 3 1/4 = 3.25 miles per day for the rest of the month. Since his running rate is greater than the other runner, they will both eventually have the same number of miles.

The difference in their running rates is 3.25 - 2.5 = 0.75 miles per day. Since the current difference between them is 15 miles, the second runner needs to run for 15 / 0.75 = 20 days.

After 20 days, the two runners will have run the same number of miles