You are training for a marathon. Currently, you can run 12 miles. You increase the distance you run on your long-run day by 7/10 mile each week. In how many more weeks will you be able to run 26 miles?

Your running distances are in an arithmetic sequence with

a = 12 , d = 7/10 or .7

you want
a + (n-1)d = 26
12 + .7(n-1) = 26
.7n - .7 = 14
.7n = 14.7
n = 21

So it will take 20 MORE weeks to reach 26 miles

To determine how many more weeks it will take for you to run 26 miles, we need to calculate how many times you need to add 7/10 mile to your current distance of 12 miles to reach 26 miles.

Let's first calculate the difference between your current distance and the target distance:

Target distance - Current distance = 26 miles - 12 miles = 14 miles

Now, let's calculate how many times you need to add 7/10 mile to your current distance:

Number of times to add 7/10 mile = Difference / Increase per week
= 14 miles / (7/10 mile per week)
= 14 miles * (10/7) weeks per mile
= 20 weeks

Therefore, you will need to add 7/10 mile to your long-run day for 20 more weeks to be able to run 26 miles.