document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209198>Question 1209198</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "It took a train 65 seconds from starting to cross an iron bridge of length 1440m to completely pass over the bridge. It also took the train 75 seconds from when it entered a 1680m tunnel to completely pass through the tunnel. <BR>\n" );
document.write( "Find the length and speed of the train.  </SPAN>\n" );
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document.write( "Answers: <BR>\n" );
document.write( "Length = <font color=red>120 meters</font><BR>\n" );
document.write( "Speed = <font color=red>86.4 kilometers per hour</font> (equivalent to <font color=red>24 meters per second</font>)\r<BR>\n" );
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document.write( "Explanation:\r<BR>\n" );
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document.write( "L = length of the train\r<BR>\n" );
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document.write( "When the tip of the train engine is just starting to cross the bridge, the back-most part of the caboose is L meters away from the start of the bridge.<BR>\n" );
document.write( "The caboose must travel this distance L, plus the length of the bridge, so that the entire train is off the bridge.<BR>\n" );
document.write( "It might be useful to make a number line drawing.\r<BR>\n" );
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document.write( "The caboose travels L+1440 meters in 65 seconds.<BR>\n" );
document.write( "distance = rate*time<BR>\n" );
document.write( "rate = distance/time<BR>\n" );
document.write( "rate = (L+1440 meters)/(65 seconds)<BR>\n" );
document.write( "rate = (L+1440)/(65) meters per second\r<BR>\n" );
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document.write( "Using similar logic, we find that the rate can also be written as (L+1680)/75 when considering the tunnel scenario.\r<BR>\n" );
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document.write( "Those two rates are assumed to be equal since we assume the train doesn't speed up nor slow down when on the bridge vs tunnel.\r<BR>\n" );
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document.write( "bridge speed = tunnel speed<BR>\n" );
document.write( "(L+1440)/65 = (L+1680)/75<BR>\n" );
document.write( "75(L+1440) = 65(L+1680)<BR>\n" );
document.write( "75L+108000 = 65L+109200<BR>\n" );
document.write( "75L-65L = 109200-108000<BR>\n" );
document.write( "10L = 1200<BR>\n" );
document.write( "L = 1200/10<BR>\n" );
document.write( "<font color=red>L = 120</font>\r<BR>\n" );
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document.write( "<font color=red>The train is 120 meters long</font>.\r<BR>\n" );
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document.write( "Then we use that length to find the train's speed<BR>\n" );
document.write( "bridge speed = (L+1440)/65<BR>\n" );
document.write( "bridge speed = (120+1440)/65<BR>\n" );
document.write( "bridge speed = <font color=red>24 meters per second</font><BR>\n" );
document.write( "or,<BR>\n" );
document.write( "tunnel speed = (L+1680)/75<BR>\n" );
document.write( "tunnel speed = (120+1680)/75<BR>\n" );
document.write( "tunnel speed = <font color=red>24 meters per second</font><BR>\n" );
document.write( "We get the same speed either way. <BR>\n" );
document.write( "You only need to show scratch work on one set rather than both. <BR>\n" );
document.write( "However, showing that both lead to the same speed helps confirm we got the correct length.\r<BR>\n" );
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document.write( "To convert from \"meters per second\" to \"kilometers per hour\", you could have this scratch work.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A%28matrix%281%2C2%2C24%2C%22meters%22%29%2Fmatrix%281%2C2%2C1%2C%22second%22%29%29%0D%0A%28matrix%281%2C2%2C3600%2C%22seconds%22%29%2Fmatrix%281%2C2%2C1%2C%22hour%22%29%29%0D%0A%28matrix%281%2C2%2C1%2C%22kilometer%22%29%2Fmatrix%281%2C2%2C1000%2C%22meters%22%29%29%0D%0A=+24%2A%283600%2F1000%29+=++matrix%281%2C4%2C86.4%2C%22kilometers%22%2C%22per%22%2C%22hour%22%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Note that 1 hour = 60*60 = 3600 seconds.<BR>\n" );
document.write( "We see that 24 meters per second = <font color=red>86.4 kilometers per hour</font>.<BR>\n" );
document.write( "Each multiplier fraction is set up so that the \"meters\" and \"seconds\" units cancel.<BR>\n" );
document.write( "The result 86.4 is exact and hasn't been rounded.<BR>\n" );
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