document.write( "Question 1204036: steve McPoke left home on his bivcycle at 8 am. traveling at 18 km/h. at 10 am, steve's brother set out after him on a motorcycle , folowing the same route. The motorcycle traveled at 54 km/h. How long had steve traveled when his brother overtok him? \n" ); document.write( "

Algebra.Com's Answer #840038 by ikleyn(52866) $\"\"$ $\"About$

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\n" ); document.write( "steve McPoke left home on his bivcycle at 8 am. traveling at 18 km/h.
\n" ); document.write( "at 10 am, steve's brother set out after him on a motorcycle , folowing the same route.
\n" ); document.write( "The motorcycle traveled at 54 km/h. How long had steve traveled when his brother overtok him?
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A quick and short \"naive\" solution

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document.write( "In 2 hours, Steve is  2*18 = 36 kilometers from the home.\r\n" );
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document.write( "Moving faster than Steve, his brother has approaching speed of 54-18 = 36 km/h.\r\n" );
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document.write( "Therefore, it is clear that the brother will overtake Steve in  = 1 hour.    \r\n" );
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document.write( "So, Steve travels 2+1 = 3 hours when the brother overtakes him.    ANSWER\r\n" );
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A slow Algebra solution

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document.write( "Let t be the time after the brother started.\r\n" );
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document.write( "So, to the catching moment, the brother moves t hours.\r\n" );
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document.write( "Steve started  earlier, so Steve moved (t+2) hours till the brother overtook him.\r\n" );
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document.write( "They cover the same distance, so we write this distance equation\r\n" );
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document.write( "    54*t = 18*(t+2)\r\n" );
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document.write( "Left side is the distance covered by the brother; right side is the distance covered by Steve.\r\n" );
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document.write( "To solve, simplify the equation. You will get\r\n" );
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document.write( "    54t = 18t + 36\r\n" );
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document.write( "Simplify and find t\r\n" );
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document.write( "   54tt - 18t = 36\r\n" );
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document.write( "       36t    = 36\r\n" );
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document.write( "          t   = 36/36 = 1  hour.\r\n" );
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document.write( "So, the brother overtakes Steve in 1 hour after the brother starts.\r\n" );
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document.write( "Steve travels 2+1 = 3 hours when the brother overtakes him.     ANSWER\r\n" );
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document.write( "You get the same answer.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved (in two different ways for your better understanding).\r
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\n" ); document.write( "\n" ); document.write( "For simple Travel & Distance problems, see introductory lessons \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 and 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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