document.write( "Question 1177753: q1) Together dien and jane eat 2/3 a pizza in 4 seconds. how long would it take each of them to eat the whole pizza alone if jane can eat a pizza 5 seconds faster than dien?\r
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\n" ); document.write( "\n" ); document.write( "q2) Baba Yaga lost her broom somewhere between her hut and Bald Mountain, and wants to get it back. She calculates that with a tailwind of 2 km/ h, she can fly from her hut to Bald Mountain in 6 hours. Baba Yaga starts her trip, finds her broom 40 km before Bald Mountain, and turns around and flies home. The entire journey takes 9 hours. Find the speed Baba Yaga flies in quiet weather (with no tailwind or headwind).\r
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Algebra.Com's Answer #806851 by ikleyn(52793) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Together they eat 2/3 pizza in 4 seconds -----------> hence, together they eat the entire pizza in 6 seconds.\r\n" );
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document.write( "Let x be the time for Dien in seconds to eat the pizza alone.\r\n" );
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document.write( "Then the time for Jane to eat the pizza alone is (x-5) seconds.\r\n" );
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document.write( "The rate of eating is    for Dien  and    for Jane in terms of entire pizza per second.\r\n" );
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document.write( "The equation for the combined rate is\r\n" );
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document.write( "     +  = .\r\n" );
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document.write( "To solve it, multiply both sides by  6x*(x-5).   You will get then\r\n" );
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document.write( "    6*(x-5)  + 6x = x*(x-5)\r\n" );
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document.write( "Reduce to the standard quadratic equation\r\n" );
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document.write( "    x^2 - 5x - 12x + 30 = 0\r\n" );
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document.write( "    x^2 - 17x + 30 = 0\r\n" );
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document.write( "Factor left side\r\n" );
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document.write( "    (x-15)*(x-2) = 0.\r\n" );
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document.write( "The only positive root x= 15 seconds for Dien provides the positive value (x-5) = 10 seconds for Jane.\r\n" );
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document.write( "ANSWER.  15 seconds for Dien and 15-5 = 10 seconds for Jane to eat the entire pizza alone.\r\n" );
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