document.write( "Question 1207791: Two bees leave two locations 150 meters apart and fly, without stopping, back and forth between these two locations at average speeds of 3 meters per second and 5 meters per second, respectively. How long is it until the bees meet for the first time? How long is it until they meet for the second time? \n" ); document.write( "

Algebra.Com's Answer #845892 by ikleyn(52852) $\"\"$ $\"About$

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\n" ); document.write( "Two bees leave two locations 150 meters apart and fly, without stopping, back and forth between
\n" ); document.write( "these two locations at average speeds of 3 meters per second and 5 meters per second, respectively.
\n" ); document.write( "(a) How long is it until the bees meet for the first time?
\n" ); document.write( "(b) How long is it until they meet for the second time?
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\n" ); document.write( "\n" ); document.write( " By default, we assume that the bees start at the same time moment.\r
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document.write( "(a)  Question (a) is simple. Initial distance is 150 meters and the rate of approaching is\r\n" );
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document.write( "     3 + 5 = 8 m/s.  So, the time till the first meeting is  150/8 = 18.75 seconds.    ANSWER\r\n" );
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document.write( "     At this point, part (a) is complete.\r\n" );
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document.write( "(b)  Faster bee covers 150 m in  150/5 = 30 seconds, and after that changes the direction to opposite.\r\n" );
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document.write( "     Slover bee covers 150 m in  150/3 = 50 seconds.\r\n" );
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document.write( "     So, when the faster bee completes 150 m in 30 seconds, the slower bee is still on the way to its turning point,\r\n" );
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document.write( "     and the slower bee will fly additional 50-30 = 20 seconds to get its turning point.\r\n" );
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document.write( "     During these 20 seconds, the faster bee, which just changed its direction to opposite,\r\n" );
document.write( "     will cover 20*5 = 100 meters.\r\n" );
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document.write( "     So, when the slower bee will reach its turning point, the distance between the bees will be 150 - 100 = 50 m.\r\n" );
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document.write( "     Now both bees fly towards each other at the approaching rate of 3+5 = 8 m/s (again).\r\n" );
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document.write( "     So, they will cover  50 m  in 50/8 = 6.25 seconds.\r\n" );
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document.write( "     Thus, the time to meet for the second time is 30 + 20 + 6.25 = 56.25 seconds (counting from the start).    ANSWER\r\n" );
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document.write( "     It is the same as to say that they will meet in the second time 56.25 - 18.75 = 37.5 seconds after their first meeting moment.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved in full, with direct, simple and straightforward consideration, with minimum calculations and with complete explanations.\r
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