Question

determining the difference in distance
points a, b, and c, form a triangle. the distance between point a and point b is 15 yards. the distance between point b and point c is 25 yards. pete walks directly from point a to point c, without passing through point b. what is the direct distance from a to c?
how far would pete walk if he went from a to b to c? blank yards
the direct distance from a to c is more than blank yards.
the inequality w < blank represents the distance, w, that pete might save by taking the direct path.

Explanation:

Step1: Calculate distance from A - B - C

Add the distance from A to B and B to C.
$15 + 25=40$ yards

Step2: Apply triangle - inequality theorem

In a triangle, the sum of the lengths of any two sides is greater than the length of the third side. Let the distance from A to C be $x$. Then $|25 - 15|\lt x\lt25 + 15$, so $x>10$ yards.

Step3: Calculate the maximum savings

The maximum distance saved $w$ by taking the direct path is when $x$ is at its minimum non - zero value greater than 10. The distance when going A - B - C is 40 yards. If $x = 10.000\cdots1$ (very close to 10), the maximum savings $w=40 - 10=30$ yards.

Answer:

How far would Pete walk if he went from A to B to C? 40 yards
The direct distance from A to C is more than 10 yards
The inequality $w < 30$ represents the distance, $w$, that Pete might save by taking the direct path.