After Karen shouts, the sound wave of her voice travels across the canyon, it hits the walls, and then it comes back to Karen in a total time of t=7.5 s. If we call L the distance between Karen and the other side of the canyon (so, L is the width of the canyon), it means that the sound wave covers a distance of S=2L in this time.
Since the wave moves by uniform motion, we can use the usual relationship between space, time and velocity:
[tex]v= \frac{S}{t}= \frac{2L}{t} [/tex]
where v=343 m/s is the speed of sound. Using this number, we can find L from the previous equation:
[tex]L= \frac{vt}{2}= \frac{(343 m/s)(7.5 s)}{2}=1286 m [/tex]
So, the canyon is 1286 meters wide.
