document.write( "Question 1122045: Hi
\n" ); document.write( "At 1pm a motorist left X travelling to Y at a uniform speed. Two hours later a bus driver started from X along the same road. The bus overtook the motorist at 6pm. The speed of the bus driver was 30kmper hour faster than the motorist.\r
\n" ); document.write( "\n" ); document.write( "Find the speed of the motorist.\r
\n" ); document.write( "\n" ); document.write( "Find the distance between X and Y if the bus was 60km from Y at 6pm.\r
\n" ); document.write( "\n" ); document.write( "thanks \n" ); document.write( "

Algebra.Com's Answer #738112 by ikleyn(52782) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "At 1 pm a motorist left X travelling to Y at a uniform speed. Two hours later a bus driver started from X along the same road.
\n" ); document.write( "The bus overtook the motorist at 6 pm. The speed of the bus driver was 30 km per hour faster than the motorist.\r
\n" ); document.write( "\n" ); document.write( "Find the speed of the motorist.\r
\n" ); document.write( "\n" ); document.write( "Find the distance between X and Y if the bus was 60km from Y at 6pm.
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document.write( "The motorist spent 5 hours on the way from the start moment at 1 pm to catching moment at 6 pm.\r\n" );
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document.write( "The bus spent 2 hours less, i.e. only 3 hours from the start to the catching moment.\r\n" );
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document.write( "Both traveled the same distance, which gives you an equation\r\n" );
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document.write( "    5*x = 3*(x+30),\r\n" );
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document.write( "where x is the motorist speed (in kilometers per hour) and (x+30) is the bus speed.\r\n" );
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document.write( "Solve the equation \r\n" );
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document.write( "    5x = 3x + 90\r\n" );
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document.write( "    3x - 3x = 90\r\n" );
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document.write( "    2x = 90  ====>  x =  = 45.\r\n" );
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document.write( "Thus the motorist speed is  45 km/k.  The bus speed is  45 + 30 = 75 km/h.\r\n" );
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document.write( "The bus traveled  3*75 = 225 kilometer.\r\n" );
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document.write( "The distance from X to Y  is  225 + 60 = 285 kilometers.\r\n" );
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document.write( "Answer.  The motorist speed was 45 kilometers per hour.\r\n" );
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document.write( "         The distance from X to Y  is  285 kilometers.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "See introductory lessons on Travel and Distance problems\r
\n" ); document.write( "\n" ); document.write( "    - Travel and Distance problems \r
\n" ); document.write( "\n" ); document.write( "    - Travel and Distance problems for two bodies moving in opposite directions \r
\n" ); document.write( "\n" ); document.write( "    - Travel and Distance problems for two bodies moving in the same direction (catching up)\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "They are written specially for you.\r
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\n" ); document.write( "\n" ); document.write( "You will find the solutions of many similar problems there.\r
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\n" ); document.write( "\n" ); document.write( "Read them and learn once for all from these lessons on how to solve simple Travel and Distance problems.\r
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\n" ); document.write( "\n" ); document.write( "Become an expert in this area.\r
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\n" ); document.write( "\n" ); document.write( "Be aware :   The solution and the answer by @josgarithmetic are both W R O N G.\r
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\n" ); document.write( "\n" ); document.write( "For your safety, simply ignore it.\r
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