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.