document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201263>Question 1201263</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "John and Kevin travel from home to school using the same route. They started at the same time. John travelled at 18km per hour. Both did not change their speeds throughout the trip. When Kevin covered 1/4  of the journey,  John was 3.5km ahead of him. If John reached school at 9.35am what time did Kevin reach school. <BR>\n" );
document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835577 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=835577\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer is <font color=red size=4>10:21:40 AM</font>\r<BR>\n" );
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document.write( "This is in the format of hours:minutes:seconds<BR>\n" );
document.write( "If the seconds don't really matter then we could round up to the nearest minute to get 10:22 AM.<BR>\n" );
document.write( "The timestamp of 10:21 AM wouldn't work because Kevin would be slightly short of arriving at his goal.\r<BR>\n" );
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document.write( "=========================================================================\r<BR>\n" );
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document.write( "Explanation:\r<BR>\n" );
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document.write( "Let's think of Kevin's journey in terms of a progress bar. <BR>\n" );
document.write( "I'll use percentages for the progress bar.\r<BR>\n" );
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document.write( "0% means Kevin is at home.<BR>\n" );
document.write( "100% means Kevin made it to school.\r<BR>\n" );
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document.write( "Attached to each percentage, I'll indicate how far John is ahead of Kevin.\r<BR>\n" );
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document.write( "0% -- John is 0 km ahead<BR>\n" );
document.write( "25% -- John is 3.5 km ahead<BR>\n" );
document.write( "50% -- John is 7 km ahead<BR>\n" );
document.write( "75% -- John is 10.5 km ahead<BR>\n" );
document.write( "100% -- John is <font color=red>14</font> km ahead\r<BR>\n" );
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document.write( "Scratch Work:<BR>\n" );
document.write( "3.5*0 = 0<BR>\n" );
document.write( "3.5*1 = 3.5<BR>\n" );
document.write( "3.5*2 = 7<BR>\n" );
document.write( "3.5*3 = 10.5<BR>\n" );
document.write( "3.5*4 = <font color=red>14</font>\r<BR>\n" );
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document.write( "The key single number to pull out of all this is the <font color=red>14</font>. <BR>\n" );
document.write( "It will come in handy in the next section below.\r<BR>\n" );
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document.write( "------------------------------------------\r<BR>\n" );
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document.write( "Now let's draw out what's going on.<BR>\n" );
document.write( "The drawing is optional, but it might be helpful for visual learners.\r<BR>\n" );
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document.write( "First we define the following locations<BR>\n" );
document.write( "A = home's location<BR>\n" );
document.write( "B = 25% of the distance from home to school<BR>\n" );
document.write( "C = Kevin's location 3.5 km ahead of point B<BR>\n" );
document.write( "D = school's location<BR>\n" );
document.write( "E = I'll explain this point later\r<BR>\n" );
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document.write( "Here's a snapshot of the start of the journey.<BR>\n" );
document.write( "Both men start at location A on the number line.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C300%2C1%2C9%2C2%2C8%2C%0D%0Agraph%28400%2C300%2C1%2C9%2C2%2C8%29%2C%0D%0Alocate%281%2C7.5%2Cmatrix%281%2C4%2C%22Kevin%27s%22%2C%22progress%22%2C%22=%22%2C%220%25%22%29%29%2C%0D%0Aline%28-3%2C5%2C13%2C5%29%2Cline%282%2C5.2%2C2%2C4.8%29%2Cline%283.2%2C5.2%2C3.2%2C4.8%29%2Cline%284.4%2C5.2%2C4.4%2C4.8%29%2Cline%285.6%2C5.2%2C5.6%2C4.8%29%2Cline%288%2C5.2%2C8%2C4.8%29%2Clocate%281.95%2C4.75%2C%22A%22%29%2Clocate%283.15%2C4.75%2C%22B%22%29%2Clocate%284.35%2C4.75%2C%22C%22%29%2Clocate%285.55%2C4.75%2C%22D%22%29%2Clocate%287.95%2C4.75%2C%22E%22%29%2C%0D%0Ared%28%0D%0Aline%282%2C3.5%2C2%2C4.3%29%2Cline%282%2C4.3%2C2.08%2C4.1614%29%2Cline%282%2C4.3%2C1.92%2C4.1614%29%2C%0D%0Alocate%281.75%2C3.5%2CJohn%29%0D%0A%29%2C%0D%0Ablue%28%0D%0Aline%282%2C6.7%2C2%2C5.5%29%2Cline%282%2C5.5%2C1.88%2C5.7078%29%2Cline%282%2C5.5%2C2.12%2C5.7078%29%2C%0D%0Alocate%281.75%2C7%2CKevin%29%0D%0A%29%2C%0D%0Alocate%281%2C2.7%2Cmatrix%281%2C2%2CDiagram%2Cnot%29%29%2C%0D%0Alocate%281%2C2.35%2Cmatrix%281%2C2%2Cto%2Cscale%29%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's fast-forward to where Kevin travels 1/4 = 25% of the journey.<BR>\n" );
document.write( "Kevin will move to point B.<BR>\n" );
document.write( "John moves to point C, which is 3.5 km further ahead compared to B.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C300%2C1%2C9%2C2%2C8%2C%0D%0Alocate%281%2C7.5%2Cmatrix%281%2C4%2C%22Kevin%27s%22%2C%22progress%22%2C%22=%22%2C%2225%25%22%29%29%2C%0D%0Aline%28-3%2C5%2C13%2C5%29%2Cline%282%2C5.2%2C2%2C4.8%29%2Cline%283.2%2C5.2%2C3.2%2C4.8%29%2Cline%284.4%2C5.2%2C4.4%2C4.8%29%2Cline%285.6%2C5.2%2C5.6%2C4.8%29%2Cline%288%2C5.2%2C8%2C4.8%29%2Clocate%281.95%2C4.75%2C%22A%22%29%2Clocate%283.15%2C4.75%2C%22B%22%29%2Clocate%284.35%2C4.75%2C%22C%22%29%2Clocate%285.55%2C4.75%2C%22D%22%29%2Clocate%287.95%2C4.75%2C%22E%22%29%2C%0D%0Ared%28%0D%0Aline%284.4%2C3.5%2C4.4%2C4.3%29%2Cline%284.4%2C4.3%2C4.48%2C4.1614%29%2Cline%284.4%2C4.3%2C4.32%2C4.1614%29%2Clocate%284.15%2C3.5%2CJohn%29%0D%0A%29%2C%0D%0Ablue%28%0D%0Aline%283.2%2C6.7%2C3.2%2C5.5%29%2Cline%283.2%2C5.5%2C3.08%2C5.7078%29%2Cline%283.2%2C5.5%2C3.32%2C5.7078%29%2Clocate%282.95%2C7%2CKevin%29%0D%0A%29%2C%0D%0Alocate%281%2C2.7%2Cmatrix%281%2C2%2CDiagram%2Cnot%29%29%2C%0D%0Alocate%281%2C2.35%2Cmatrix%281%2C2%2Cto%2Cscale%29%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The gap from B to C is 3.5 km.<BR>\n" );
document.write( "BC = 3.5\r<BR>\n" );
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document.write( "Now let's fast-forward to when John arrives at school.<BR>\n" );
document.write( "John moves to point D and it is 9:35 AM.<BR>\n" );
document.write( "Kevin is somewhere between B and D, excluding either endpoint.<BR>\n" );
document.write( "This is what that looks like:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C300%2C1%2C9%2C2%2C8%2C%0D%0Alocate%281%2C7.5%2Cmatrix%281%2C8%2C%22Kevin%27s%22%2C%22progress%22%2C%22=%22%2C%22somewhere%22%2C%22between%22%2C%2225%25%22%2C%22and%22%2C%22100%25%22%29%29%2C%0D%0Alocate%285%2C7%2Cmatrix%281%2C2%2C%22%28excluding%22%2C%22endpoints%29%22%29%29%2C%0D%0Aline%28-3%2C5%2C13%2C5%29%2Cline%282%2C5.2%2C2%2C4.8%29%2Cline%283.2%2C5.2%2C3.2%2C4.8%29%2Cline%284.4%2C5.2%2C4.4%2C4.8%29%2Cline%285.6%2C5.2%2C5.6%2C4.8%29%2Cline%288%2C5.2%2C8%2C4.8%29%2Clocate%281.95%2C4.75%2C%22A%22%29%2Clocate%283.15%2C4.75%2C%22B%22%29%2Clocate%284.35%2C4.75%2C%22C%22%29%2Clocate%285.55%2C4.75%2C%22D%22%29%2Clocate%287.95%2C4.75%2C%22E%22%29%2C%0D%0Ared%28%0D%0Aline%285.6%2C3.5%2C5.6%2C4.3%29%2Cline%285.6%2C4.3%2C5.68%2C4.1614%29%2Cline%285.6%2C4.3%2C5.52%2C4.1614%29%2Clocate%285.35%2C3.5%2CJohn%29%2Clocate%285%2C2.35%2Cmatrix%281%2C2%2C%229%3A35%22%2C%22AM%22%29%29%0D%0A%29%2C%0D%0Ablue%28%0D%0Aarc%283.44%2C5.44%2C0.48%2C0.48%2C180%2C270%29%2Cline%283.44%2C5.68%2C4.16%2C5.68%29%2Carc%284.16%2C5.92%2C0.48%2C0.48%2C0%2C90%29%2Carc%284.64%2C5.92%2C0.48%2C0.48%2C90%2C180%29%2Cline%284.64%2C5.68%2C5.36%2C5.68%29%2Carc%285.36%2C5.44%2C0.48%2C0.48%2C270%2C360%29%2C%0D%0Alocate%284.15%2C6.5%2CKevin%29%0D%0A%29%2C%0D%0Alocate%281%2C2.7%2Cmatrix%281%2C2%2CDiagram%2Cnot%29%29%2C%0D%0Alocate%281%2C2.35%2Cmatrix%281%2C2%2Cto%2Cscale%29%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Technically John should stop when reaching point D.<BR>\n" );
document.write( "However, I'll have him keep moving to reach point E.\r<BR>\n" );
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document.write( "Once John reaches point E, Kevin will have arrived at point D.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C300%2C1%2C9%2C2%2C8%2C%0D%0Alocate%281%2C7.5%2Cmatrix%281%2C4%2C%22Kevin%27s%22%2C%22progress%22%2C%22=%22%2C%22100%25%22%29%29%2C%0D%0Aline%28-3%2C5%2C13%2C5%29%2Cline%282%2C5.2%2C2%2C4.8%29%2Cline%283.2%2C5.2%2C3.2%2C4.8%29%2Cline%284.4%2C5.2%2C4.4%2C4.8%29%2Cline%285.6%2C5.2%2C5.6%2C4.8%29%2Cline%288%2C5.2%2C8%2C4.8%29%2Clocate%281.95%2C4.75%2C%22A%22%29%2Clocate%283.15%2C4.75%2C%22B%22%29%2Clocate%284.35%2C4.75%2C%22C%22%29%2Clocate%285.55%2C4.75%2C%22D%22%29%2Clocate%287.95%2C4.75%2C%22E%22%29%2C%0D%0Ared%28%0D%0Aline%288%2C3.5%2C8%2C4.3%29%2Cline%288%2C4.3%2C8.08%2C4.1614%29%2Cline%288%2C4.3%2C7.92%2C4.1614%29%2Clocate%287.75%2C3.5%2CJohn%29%2C%0D%0Alocate%285%2C2.35%2Cmatrix%281%2C5%2Csome%2Ctime%2Cafter%2C%229%3A35%22%2C%22AM%22%29%29%0D%0A%29%2C%0D%0Ablue%28%0D%0Aline%285.6%2C6.7%2C5.6%2C5.5%29%2Cline%285.6%2C5.5%2C5.48%2C5.7078%29%2Cline%285.6%2C5.5%2C5.72%2C5.7078%29%2Clocate%285.35%2C7%2CKevin%29%0D%0A%29%2C%0D%0Alocate%286.5%2C5.4%2C+matrix%281%2C2%2C14%2Ckm%29%29%2C%0D%0Alocate%281%2C2.7%2Cmatrix%281%2C2%2CDiagram%2Cnot%29%29%2C%0D%0Alocate%281%2C2.35%2Cmatrix%281%2C2%2Cto%2Cscale%29%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Point E is 14 km ahead of point D.<BR>\n" );
document.write( "This was the 14 I mentioned earlier.\r<BR>\n" );
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document.write( "Let's determine how long it takes for John to travel that extra 14 km.<BR>\n" );
document.write( "distance = rate*time<BR>\n" );
document.write( "time = distance/rate<BR>\n" );
document.write( "time = 14/18<BR>\n" );
document.write( "time = 7/9 of an hour<BR>\n" );
document.write( "This is the time it takes for John to move from point D to point E.<BR>\n" );
document.write( "This time value is added onto the time of 9:35 AM to determine when Kevin arrives at school.\r<BR>\n" );
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document.write( "To have 7/9 of an hour make more sense, let's first convert to minutes:seconds format.<BR>\n" );
document.write( "1 hr = 60*60 = 3600 sec<BR>\n" );
document.write( "7/9 hrs = (7/9)*3600 = 2800 sec<BR>\n" );
document.write( "2800/60 = 46.6666666666667<BR>\n" );
document.write( "46 min = 46*60 = 2760 sec<BR>\n" );
document.write( "2800 sec = 2760 sec + 40 sec<BR>\n" );
document.write( "2800 sec = 46 min + 40 sec<BR>\n" );
document.write( "Therefore,<BR>\n" );
document.write( "7/9 of an hour = 46 min + 40 sec\r<BR>\n" );
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document.write( "We'll add the duration \"46 min + 40 sec\" onto the starting time of 9:35 AM to determine the final answer.\r<BR>\n" );
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document.write( "The jump from 9:35 AM to 10:00 AM is 25 minutes.<BR>\n" );
document.write( "The remaining 46-25 = 21 minutes has us go from 10:00 AM to 10:21 AM<BR>\n" );
document.write( "Then we have an additional 40 seconds tacked on at the end.\r<BR>\n" );
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document.write( "Final Answer is <font color=red size=4>10:21:40 AM</font><BR>\n" );
document.write( "This is in the format of hours:minutes:seconds<BR>\n" );
document.write( "If the seconds don't really matter then we could round up to the nearest minute to get 10:22 AM.<BR>\n" );
document.write( "The timestamp of 10:21 AM wouldn't work because Kevin would be slightly short of arriving at his goal.<BR>\n" );
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