The sum of the distances two hikers walked is 53 mi, and the difference is 25 mi. What are the distances?
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a + b = 53
a - b = 25
a = 53 - b
53 - b - b = 25
-2b = 25 - 53
-b = -28/2
b = 14
a = 53 - 14
a = 39
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To find the distances walked by the two hikers, we can set up a system of linear equations based on the given information.
Let's assume that the distance walked by one hiker is 'x' miles, and the distance walked by the other hiker is 'y' miles.
According to the problem, the sum of the distances is 53 miles, so we can write the equation:
x + y = 53 ---(Equation 1)
Also, the difference between the distances is 25 miles, so we can write another equation:
x - y = 25 ---(Equation 2)
To solve this system of equations, we can use the method of substitution or elimination.
Let's solve it using the elimination method. Add Equation 1 and Equation 2 together:
(x + y) + (x - y) = 53 + 25
2x = 78
x = 39
Now that we have the value of 'x' as 39, we can substitute it back into either Equation 1 or Equation 2 to find the value of 'y'. Let's use Equation 1:
39 + y = 53
y = 53 - 39
y = 14
Therefore, the distances walked by the two hikers are 39 miles and 14 miles respectively.