document.write( "Question 825045: A train X leaves Meerut at 5a.m and reaches Delhi at 9a.m. Another train Y leaves Delhi at 7a.m and reaches Meerut at 10:30a.m . At what time do the two trains cross one another? \n" ); document.write( "

Algebra.Com's Answer #496972 by Edwin McCravy(20060) $\"\"$ $\"About$

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A train X leaves Meerut at 5a.m and reaches Delhi at 9a.m. Another train Y leaves Delhi at 7a.m and reaches Meerut at 10:30a.m . At what time do the two trains cross one another?
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document.write( "Suppose it is N km from Meerut to Delhi\r\n" );
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document.write( "Train X travels N km in 4 hours, so X's speed is N/4 km/hr\r\n" );
document.write( "Train Y travels N km in  or  hours, so Y's speed \r\n" );
document.write( "is N÷ = N× = 2N/7 km/hr \r\n" );
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document.write( "Let t = the time after 7a.m. that train Y travels\r\n" );
document.write( "Then, t+2 = the time after 5a.m. that train X travels\r\n" );
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document.write( "        |   speed × time  =  distance\r\n" );
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document.write( "train X |    N/4  |  t+2  | (N/4)(t+2)     \r\n" );
document.write( "train Y |   2N/7  |   t   |   2Nt/7\r\n" );
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document.write( "Equation:\r\n" );
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document.write( "   Train X's distance + Train Y's distance = N km\r\n" );
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document.write( "                     (t+2) +  = N\r\n" );
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document.write( "Multiply by LCM = 28\r\n" );
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document.write( "                     7N(t+2) + 8Nt = 28N\r\n" );
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document.write( "Divide by N\r\n" );
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document.write( "                       7(t+2) + 8t = 28  \r\n" );
document.write( "                      7t + 14 + 8t = 28\r\n" );
document.write( "                          15t + 14 = 28\r\n" );
document.write( "                               15t = 14\r\n" );
document.write( "                                 t = 14/15 hr = (14/15)×60 = 56 min.\r\n" );
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document.write( "56 minutes after 7a.m. is 7:56a.m. \r\n" );
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document.write( "Edwin\r\n" );
document.write( "[It is only 88 km from Meerut to Delhi, so both trains are very slow! :) ]   \r\n" );
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