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Sounds travels about 750 miles per hour. If you stand in a canyon and sound a horn, you will hear an echoSuppose it takes about 3 second to hear the echo. How far away is the canyon wall, in feet Now let’s generalize that result. Suppose it takes n seconds to hear echo. How far away is the canyon wall in terms of n?

Answer :

The time it takes to hear an echo can be gotten from the equation;

[tex]t=\frac{2D}{v}[/tex]

Where D is the distance to the wall, v is the speed of sound which is 750 miles per hour.

If it takes 3 seconds to hear an echo, the distance can be gotten by rewriting the equation as;

[tex]D=\frac{vt}{2}[/tex]

Therefore, we find out that;

[tex]D=\frac{750\times3}{2}=1125\text{miles.}[/tex]

Therefore, the wall is 1125 miles away.

b. To generalize the result;

If it takes n seconds to hear an echo, the distance to the canyon wall is;

[tex]D=\frac{750n}{2}=375n[/tex]

Therefore, D = 375n

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