Chapter 6.1, Problem 18P

The sum of the distances two hikers walked is 53 mi, and the difference is 25 mi. What are the distances?

To determine

To find: The distances walked by two hikers.

Answer to Problem 18P

The distances they walked are 39 mi and 14 mi.

Explanation of Solution

Given information:The sum of the distances two hikers walked is 53 mi and the difference is 25 mi.

Calculation:

Let one hiker walked for ‘ x’ miles

Another hiker walked for ‘ y’ miles.

According to the given information the two equations are

  $x+y=53$

  $x-y=25$

Solve the system of equations using elimination method.

Add the equations to get rid the y terms.

  $\begin{array}{l}x+y=53\\ x-y=25\\ ------\\ 2x=78\end{array}$

Divide both sides by 2.

  $x=39$

Substitute x as 39 into any of the equations to find the y .

  $39+y=53$

Subtract both sides 39.

  $y=14$

That’s one hiker walked for 39 mi and other hiker walked for 14 mi.

Conclusion: The distances are 39 mi and 14 mi.