Question

school life bryan is at the library doing a research paper. he leaves the library at point a and walks to the soccer field for a game at point c. the supermarket at point b is exactly halfway between the library and the soccer field. after bryans first soccer game, he walks to the supermarket to buy a snack, and then he walks back to the soccer field for his second game. not including the time spent at the soccer games, how far does bryan walk?

Explanation:

Step1: Define distances

Let the distance from library (point A) to soccer - field (point C) be \(d = AC\). Since point B (supermarket) is halfway between A and C, \(AB=BC=\frac{d}{2}\).

Step2: Analyze Bryan's path

Bryan first walks from A to C, distance \(d\). Then he walks from C to B, distance \(\frac{d}{2}\), and then from B to C, distance \(\frac{d}{2}\).

Step3: Calculate total distance

The total distance \(D\) he walks is \(d+\frac{d}{2}+\frac{d}{2}\). Substituting and simplifying, \(D = d + d=2d\).

Answer:

Twice the distance from the library to the soccer - field.