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April 26th, 2014, 03:07 PM   #1
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Algebra word problem

The speed of sound in an iron rod is 16,850 ft/sec, and the speed in air is 1100 ft/sec. If a sound originating at one end of the rod is heard one second sooner through the rod than through the air, how long is the rod?

Please explain a full explanation to the solution that you come up with.
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April 26th, 2014, 05:32 PM   #2
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Distance = Velocity x Time

And in the case of both air and iron, the distance is the same. We have both velocities and we can write $t_{air} = t_{iron} + 1$.

Thus, we have
\begin{align*}
\frac{d}{v_{air}} &= t_{iron} + 1 \\
\frac{d}{v_{iron}} &= t_{iron} \\
d\left(\frac{1}{v_{air}} - \frac{1}{v_{iron}}\right) &= 1 \\
\end{align*}
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April 26th, 2014, 06:09 PM   #3
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16850x - 1100x = 1100, x = 22/315. 22/315 * 16850 = 74140/63.
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