document.write( "Question 1192052: Triplets Peter, Reeta and Nikita have two ways for getting home from school each day: cycle on a tandem bike or walk. The bike can carry either one or two riders at a time. Regardless of the number of people pedalling, cycling speed is 5 times walking speed. The triplets always leave school at the same time and always use the same path between school and home, whether walking or cycling. The school is 5 km from home and their walking speed is 4 kilometres per hour.\r
\n" ); document.write( "\n" ); document.write( "a) On Monday, Nikita and Peter cycle and Reeta walks. On reaching the point four-fifths of the way home the bike gets a puncture, so Nikita and Peter walk the rest of the way home. How far from school is Peeta when the cyclists arrive home?\r
\n" ); document.write( "\n" ); document.write( "b) On Tuesday, Peter and Reeta ride the bike and Nikita walks. When the cyclists arrive home, Peter hops off the bike and Reeta rides back towards school to collect Nikita. How far from school is Nikita when Reeta reaches her?\r
\n" ); document.write( "\n" ); document.write( "c) On Wednesday, Reeta and Nikita take the bike and Peter walks. When the cyclists are halfway home, Reeta hops off and walks the rest of the way, while Nikita heads back to pick up Peter. How far from school is Reeta when her siblings pass her on the bike?\r
\n" ); document.write( "\n" ); document.write( "d) On Thursday, it is Reeta's turn to walk. Peter drops Nikita off at a certain point leaving her to walk home. Meanwhile he returns to pick up Reeta and they cycle home together. If all three arrive home at the same time, how far from school are the drop-off and pick-up points? \n" ); document.write( "

Algebra.Com's Answer #851836 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "Triplets Peter, Reeta and Nikita have two ways for getting home from school each day: cycle on a tandem bike or walk.
\n" ); document.write( "The bike can carry either one or two riders at a time.
\n" ); document.write( "Regardless of the number of people pedalling, cycling speed is 5 times walking speed.
\n" ); document.write( "The triplets always leave school at the same time and always use the same path between school and home,
\n" ); document.write( "whether walking or cycling. The school is 5 km from home and their walking speed is 4 kilometres per hour.\r
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\n" ); document.write( "\n" ); document.write( "a) On Monday, Nikita and Peter cycle and Reeta walks. On reaching the point four-fifths of the way home
\n" ); document.write( "the bike gets a puncture, so Nikita and Peter walk the rest of the way home. How far from school is Peeta when the cyclists arrive home?\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "b) On Tuesday, Peter and Reeta ride the bike and Nikita walks. When the cyclists arrive home,
\n" ); document.write( "Peter hops off the bike and Reeta rides back towards school to collect Nikita. How far from school is Nikita when Reeta reaches her?\r
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\n" ); document.write( "\n" ); document.write( "c) On Wednesday, Reeta and Nikita take the bike and Peter walks. When the cyclists are halfway home,
\n" ); document.write( "Reeta hops off and walks the rest of the way, while Nikita heads back to pick up Peter.
\n" ); document.write( "How far from school is Reeta when her siblings pass her on the bike?\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "d) On Thursday, it is Reeta's turn to walk. Peter drops Nikita off at a certain point leaving her to walk home.
\n" ); document.write( "Meanwhile he returns to pick up Reeta and they cycle home together. If all three arrive home at the same time,
\n" ); document.write( "how far from school are the drop-off and pick-up points?
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\n" ); document.write( "\n" ); document.write( "        In the solution by @CPhill to this problem, his interpretation for part (d) is CERTAINLY incorrect.\r
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\n" ); document.write( "\n" ); document.write( "        The correct interpretation for part (d), from the problem, is that first Peter and Nikita are cycling, \r
\n" ); document.write( "\n" ); document.write( "        while Reeta is $\"highlight%28highlight%28walking%29%29\"$ - - - not waiting at the school.\r
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\n" ); document.write( "\n" ); document.write( "        Then Peter drops Nikita off at a certain point leaving her to walk home, and Peter returns back \r
\n" ); document.write( "\n" ); document.write( "        to pick up Reeta on her way to the home.\r
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\n" ); document.write( "\n" ); document.write( "        After that, Peter and Reeta are cycling home together.\r
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\n" ); document.write( "\n" ); document.write( "        It is the ONLY one and the UNIQUE possible interpretation, and the text points it directly, saying in (d) that \r
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\n" ); document.write( "\n" ); document.write( "                \" On Thursday, it is Reeta's turn to walk \".\r
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\n" ); document.write( "\n" ); document.write( "        It is a classic Travel and Distance problem, which I know along and across from my school years.\r
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\n" ); document.write( "\n" ); document.write( "                        So, below is my solution for part (d) in this correct interpretation.\r
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document.write( "So, the distance from the school to home is 5 km; walking speed is 4 km/h  and the cycling speed is 20 km/h.\r\n" );
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document.write( "Let x be the distance from the school to the drop-off point and \r\n" );
document.write( "let y be the distance from the school to the pick-up point.\r\n" );
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document.write( "The time for Peter to get the drop-off point is    hours.\r\n" );
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document.write( "The time for Peter to move from the drop-off point to pick-up point is    hours.\r\n" );
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document.write( "The time for Peter to get the drop-off point and then to return to the pick-up point is the sum\r\n" );
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document.write( "     = .   (1)\r\n" );
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document.write( "This time,   hours, is equal to the time for Reeta to get the pick-up pont from the school,  which is   hours.\r\n" );
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document.write( "It gives us this equation\r\n" );
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document.write( "     = .    (2)\r\n" );
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document.write( "Simplify it\r\n" );
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document.write( "    4(2x-y) = 20y,   or  2x-y = 5y,  or  2x = 5y + y,  or  2x = 6y,  or  x = 3y.    (3).\r\n" );
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document.write( "    +------------------------------------------------------------------------+\r\n" );
document.write( "    |     At this point, we complete our consideration for moving Peter      |\r\n" );
document.write( "    |  from the school to the drop-off point and then to the pick-up point.  |\r\n" );
document.write( "    +------------------------------------------------------------------------+\r\n" );
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document.write( "Now we will consider the other part of moving.\r\n" );
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document.write( "The time for Nikita to get the home from the drop-off point walking is    hours.\r\n" );
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document.write( "During this time, Peter is cycling from point x to point y and then from point y to the home.\r\n" );
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document.write( "It takes for Peter   +  =   hours.\r\n" );
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document.write( "The time   for Nikita is the same as the time    for Peter.\r\n" );
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document.write( "It gives us this equation\r\n" );
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document.write( "     = .    (4)\r\n" );
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document.write( "Simplify it\r\n" );
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document.write( "    20(5-x) = 4(5+x- 2y),  or  100-20x = 20+4x-8y,  or  100-20 = 4x + 20x-8y,  or  24x-8y = 80,  or  3x - y = 10.    (5)\r\n" );
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document.write( "Thus, we have now two equations\r\n" );
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document.write( "    x = 3y  and  3x - y = 10.\r\n" );
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document.write( "Substitute first equation,  x = 3y, into the second equation\r\n" );
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document.write( "    3*(3y) - y = 10,  or  9y - y = 10,  8y = 10,  y =  =  = 1.25.\r\n" );
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document.write( "Then  x = 3y = 3*1.25 = 3.75.\r\n" );
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document.write( "Thus  the drop-off point is 3.75 km from the school, and the pick-up point is 1.25 km from the school.   ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "At this point, the part (d) of the problem is solved completely.\r
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\n" ); document.write( "\n" ); document.write( " Regarding the post by @CPhill . . . \r
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\n" ); document.write( "\n" ); document.write( "Keep in mind that @CPhill is a pseudonym for the Google artificial intelligence.\r
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\n" ); document.write( "\n" ); document.write( "The artificial intelligence is like a baby now. It is in the experimental stage
\n" ); document.write( "of development and can make mistakes and produce nonsense without any embarrassment.\r
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\n" ); document.write( "\n" ); document.write( " It has no feeling of shame - it is shameless.\r
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\n" ); document.write( "\n" ); document.write( "This time, again, it made an error.\r
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\n" ); document.write( "\n" ); document.write( "Although the @CPhill' solution are copy-paste Google AI solutions, there is one essential difference.\r
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\n" ); document.write( "\n" ); document.write( "Every time, Google AI makes a note at the end of its solutions that Google AI is experimental
\n" ); document.write( "and can make errors/mistakes.\r
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\n" ); document.write( "\n" ); document.write( "All @CPhill' solutions are copy-paste of Google AI solutions, with one difference:
\n" ); document.write( "@PChill never makes this notice and never says that his solutions are copy-past that of Google.
\n" ); document.write( "So, he NEVER SAYS TRUTH.\r
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\n" ); document.write( "\n" ); document.write( "Every time, @CPhill embarrassed to tell the truth.\r
\n" ); document.write( "\n" ); document.write( "But I am not embarrassing to tell the truth, as it is my duty at this forum.\r
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\n" ); document.write( "\n" ); document.write( "And the last my comment.\r
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\n" ); document.write( "\n" ); document.write( "When you obtain such posts from @CPhill, remember, that NOBODY is responsible for their correctness,
\n" ); document.write( "until the specialists and experts will check and confirm their correctness.\r
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\n" ); document.write( "\n" ); document.write( "Without it, their reliability is ZERO and their creadability is ZERO, too.\r
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