the sum of the distances two hikers walked is 53 miles, and the difference is 25 miles. what are the distances

To solve this problem, you can create a system of equations and solve for each hiker's distance walked.

Hiker 1 distance walked: x
Hiker 2 distance walked: y

Their combined distance walked is 53 miles, thus - 
x + y = 53

The difference between miles walked is 25, thus - 
x - 25 = y

Let's solve using substitution. To do that, substitute x - 23 into x + y = 53 for y.

x + y = 53
x + (x - 25) = 53
x + x - 25 = 53
2x - 25 = 53
2x = 78
x = 39

To find y, substitute 39 for x into either of the equations.

x + y = 53
39 + y = 53
y = 14

Finally, check all work.

x + y = 53
39 + 14 = 53
53 = 53

x - 25 = y
39 - 25 = 14
14 = 14

Answer:
One hiker walked 39 miles and the other hiker walked 14 miles.