document.write( "Question 1163467: Sam drives from City A to City B, and he takes 8 hours for the entire trip.
\n" ); document.write( "Richard drives from City B to City A, and he takes 10 hours for the trip
\n" ); document.write( "assuming they are driving on the same road. If Sam leaves City A and Richard
\n" ); document.write( "leaves City B at the same time, how many hours will they meet at a place 40
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Algebra.Com's Answer #787659 by MathTherapy(10552)\"\" \"About 
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Sam drives from City A to City B, and he takes 8 hours for the entire trip.
\n" ); document.write( "Richard drives from City B to City A, and he takes 10 hours for the trip
\n" ); document.write( "assuming they are driving on the same road. If Sam leaves City A and Richard
\n" ); document.write( "leaves City B at the same time, how many hours will they meet at a place 40
\n" ); document.write( "km away from the halfway? Express your answer as a mixed number.
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Oh well, someone beat me to this one!!\r\n" );
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document.write( "Finding TIME, IMMEDIATELY\r\n" );
document.write( "Since Sam takes 8 hours to complete the trip, while Richard takes 10 hours, “needless to say,” Sam’s speed is greater \r\n" );
document.write( "than Richard’s, which means that Sam will get to the 40-km mark, on Richard’s side, after passing the ½-way mark\r\n" );
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document.write( "Let time taken by both to get to 40 kms beyond the ½-way point, from A, be T, and let distance from A to B, or from B to A, be 2D\r\n" );
document.write( "Then the ½-way point is 2D/2 = D, and Sam will travel a distance of D + 40, while Richard will travel a distance of D - 40\r\n" );
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document.write( "Since Sam takes 8 hours to complete the trip, then Sam’s speed = \"matrix%281%2C3%2C+2D%2F8%2C+%22=%22%2C+D%2F4+%29\"\r\n" );
document.write( "Since Richard takes 10 hours to complete the trip, his speed, from B to A, is \"matrix%281%2C3%2C+2D%2F10%2C+%22=%22%2C+D%2F5%29\"\r\n" );
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document.write( "We then get the following SPEED equations for:\r\n" );
document.write( "      Sam                       and                  Richard \r\n" );
document.write( "                             \r\n" );
document.write( "   \"matrix%281%2C3%2C+160%2F%28T++-++4%29%2C+%22=%22%2C+D%29\" ------ eq (i)                           \"matrix%281%2C3%2C+D%2C+%22=%22%2C+200%2F%285++-++T%29%29\" ------ eq (ii)\r\n" );
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document.write( "With \"matrix%281%2C3%2C+D%2C+%22=%22%2C+160%2F%28T++-++4%29%29\", and \"matrix%281%2C3%2C+D%2C+%22=%22%2C+200%2F%285++-++T%29%29\", we can say that: \"matrix%281%2C3%2C+160%2F%28T++-++4%29%2C+%22=%22%2C+200%2F%285++-++T%29%29\"\r\n" );
document.write( "200(T - 4) = 160(5 - T) ------ Cross-multiplying\r\n" );
document.write( "40(5)(T - 4) = 40(4)(5 - T)\r\n" );
document.write( "5(T - 4) = 4(5 - T)\r\n" );
document.write( "5T - 20 = 20 - 4T\r\n" );
document.write( "5T + 4T = 20 + 20\r\n" );
document.write( "9T = 40\r\n" );
document.write( "T, or time taken by both to get to 40 kms beyond the ½-way point, from A is: \"highlight_green%28matrix%281%2C4%2C+40%2F9%2C+or%2C+4%264%2F9%2C+hours%29%29\" \r\n" );
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document.write( "OR\r\n" );
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document.write( "Finding Sam’s SPEED, in order to get the answer: TIME\r\n" );
document.write( "Since Sam takes 8 hours to complete the trip, while Richard takes 10 hours, “needless to say,” Sam’s speed is greater\r\n" );
document.write( "than Richard’s, which means that Sam will get to the 40-km mark, on Richard’s side, after passing the ½-way mark\r\n" );
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document.write( "Let Sam’s speed be S\r\n" );
document.write( "Since Sam takes 8 hours to complete the trip, then distance, from A to B, or from B to A, is 8S\r\n" );
document.write( "Since Richard takes 10 hours to complete the trip, his speed, from B to A, is \"matrix%281%2C3%2C+8S%2F10%2C+%22=%22%2C+4S%2F5%29\"\r\n" );
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document.write( "As the distance is 8S, the ½-way point is: \"matrix%281%2C3%2C+8S%2F2%2C+%22=%22%2C+4S%29\", and with Sam’s speed being greater than Richard’s, Sam will travel to the 40-km mark, on “Richard’s side,” after passing the ½-way point. \r\n" );
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document.write( "As such, distance Sam will have traveled to get to 40 kms past the half-way point: 4S + 40, AND\r\n" );
document.write( "         distance Richard will have traveled to get to “Sam’s point”: 8S - (4S + 40) = 4S - 40\r\n" );
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document.write( "Time Sam takes to travel to 40 kms past the half-way point (on Richard’s side): \"%284S+%2B+40%29%2FS\"\r\n" );
document.write( "Time Richard takes to travel to “Sam’s point”: \"%284S++-++40%29%2F%284S%2F5%29\"\r\n" );
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document.write( "Since they left at the same time, then their times will be the same, to get to \"Sam's point.\" Therefore, we get: \r\n" );
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document.write( "4S + 40 = 5(S - 10) ------ Denominators are equal and so are the numerators\r\n" );
document.write( "4S + 40 = 5S - 50\r\n" );
document.write( "4S - 5S = - 50  -  40\r\n" );
document.write( "- S = - 90\r\n" );
document.write( "Sam’s speed, or \r\n" );
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document.write( "Travelling 40 kms past the halfway mark (on “Richard’s side) - a distance of 4S + 40, or 4(90) + 40 = 400 kms, at S (90) km/h, or 400 km @ 90 km/h - time Sam takes is: \r\n" );
document.write( "OR\r\n" );
document.write( "Travelling a distance of 4S - 40, or 4(90) - 40 = 320 kms, at \"matrix%281%2C5%2C+4S%2F5%2C+%22=%22%2C+4%2890%29%2F5%2C+%22=%22%2C+72%29\", or 320 kms @ 72 km/h - time Richard takes is:
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