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April 26th, 2014, 03:07 PM  #1 
Senior Member Joined: Feb 2014 From: Louisiana Posts: 156 Thanks: 6 Math Focus: algebra and the calculus  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. 
April 26th, 2014, 05:32 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,681 Thanks: 2659 Math Focus: Mainly analysis and algebra 
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*} 
April 26th, 2014, 06:09 PM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond 
16850x  1100x = 1100, x = 22/315. 22/315 * 16850 = 74140/63.


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