<p>A spike is hammered into a train rail. You are standing at the other end of the rail. You hear the sound of the hammer strike both through the air and through the rail itself. These sounds arrive at your point six seconds apart. You know that sound travels through air at 1100 feet per second and through steel at 16,500 feet per second. How far away is that spike?</p>
<p>Okay, so you know that Distance = Rate * Time, or d = rt.</p>
<p>Well you know the rate of travel thru the air which is 1100ft\s, and you know the speed of travel thru the steel, which is 16,500 ft per second. The hitting sound travels through the steel faster, so you know it will reach you first. That means the sound in the air will reach you 6 seconds later.</p>
<p>Distance = 1100ft\s * ( T + 6)
and
Distance = 16,500ft\s * T</p>
<p>where distance is the distance between you and the hammering, and Time is how long it takes to reach you. It makes sense that if the sound travels thru the metal and takes T time, then it takes T+6 for the sound to reach you in the air as it stated.</p>
<p>Make them equal, 1100( T + 6) = 16500T , 1100T + 6600 = 16500T , subtract</p>
<p>15400T = 6600. Divide by 15400 to get T = 3\7 seconds or .428. The distance = rate * time, so 15400*(3\7) = </p>
<p>7071 feet.</p>
<p>D=distance
VS=velocity through steel
VA=velocity through air
ts=time through steel
ta=time through air</p>
<p>Let’s just get some equations out there:
D=VS<em>ts=16500</em>ts
D=VA<em>ta=1100</em>ta
ta=ts+6 (you can reason that it will take longer through air because the speed is slower)</p>
<p>So, D=16500<em>ts=1100</em>ta=D so 16500<em>ts=1100</em>ta. Substituting ts+6 in for ta we get 16500<em>ts=1100</em>(ts+6), so 16500<em>ts=1100</em>ts+6600. Subtracting 1100<em>ts from both sides, we get 15400</em>ts=6600, so ts=6600/15400=3/7 seconds. So, to find the distance, we need only plug this time back into the equation D=16500<em>ts=16500</em>3/7=7071.43 feet.</p>
<p>dang, cjone beat me to it :(</p>
<p>I’m guessing this isn’t a CB question</p>
<p>^why not ?</p>
<p>You can tell by the wording</p>
<p>Thanks the answer is correct. cjgone I think you made a small typo, no big deal, I understand the solution now!</p>