document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192052>Question 1192052</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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<BR>\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<BR>\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<BR>\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<BR>\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? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849089 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849089\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to solve this problem:\r<BR>\n" );
document.write( "\n" );
document.write( "**a) Monday:**\r<BR>\n" );
document.write( "\n" );
document.write( "1. **Walking speed:** 4 km/h<BR>\n" );
document.write( "2. **Cycling speed:** 4 km/h * 5 = 20 km/h<BR>\n" );
document.write( "3. **Distance cycled:** (4/5) * 5 km = 4 km<BR>\n" );
document.write( "4. **Time taken to cycle:** 4 km / 20 km/h = 0.2 hours<BR>\n" );
document.write( "5. **Distance walked by Reeta:** 4 km/h * 0.2 hours = 0.8 km<BR>\n" );
document.write( "6. **Distance remaining for Reeta:** 5 km - 0.8 km = 4.2 km<BR>\n" );
document.write( "7. **Time taken to walk the remaining distance:** 4.2 km / 4 km/h = 1.05 hours<BR>\n" );
document.write( "8. **Total time taken by cyclists (and Reeta):** 0.2 hours + 1.05 hours = 1.25 hours<BR>\n" );
document.write( "9. **Distance walked by Reeta in total:** 4 km/h * 1.25 hours= 5km<BR>\n" );
document.write( "10. **When the cyclists arrive home, Reeta is already home.**\r<BR>\n" );
document.write( "\n" );
document.write( "**b) Tuesday:**\r<BR>\n" );
document.write( "\n" );
document.write( "1. **Time taken by cyclists to reach home:** 5 km / 20 km/h = 0.25 hours<BR>\n" );
document.write( "2. **Distance walked by Nikita:** 4 km/h * 0.25 hours = 1 km<BR>\n" );
document.write( "3. **Distance remaining for Nikita:** 5 km - 1 km = 4 km<BR>\n" );
document.write( "4. **Time taken by Reeta to cycle back to collect Nikita:**  Let 't' be the time.  Reeta cycles 20t km and Nikita walks 4t km. The distance they cover together must equal the remaining distance of Nikita. So, 20t + 4t = 4 => t = 4/24=1/6 hours<BR>\n" );
document.write( "5. **Distance covered by Nikita during this time:** 4 km/h * (1/6) hours = 2/3 km<BR>\n" );
document.write( "6. **Total distance walked by Nikita:** 1 km + (2/3) km = 5/3 km<BR>\n" );
document.write( "7. **Distance from school when Reeta reaches her:** 5 km - (5/3) km = 10/3 km = 3.33 km\r<BR>\n" );
document.write( "\n" );
document.write( "**c) Wednesday:**\r<BR>\n" );
document.write( "\n" );
document.write( "1. **Time taken by cyclists to reach halfway point:** 2.5 km / 20 km/h = 0.125 hours<BR>\n" );
document.write( "2. **Distance walked by Peter:** 4 km/h * 0.125 hours = 0.5 km<BR>\n" );
document.write( "3. **Distance remaining for Peter:** 5 km - 0.5 km = 4.5 km<BR>\n" );
document.write( "4. **Let 't' be the time taken for Nikita to cycle back and meet Peter.** Nikita cycles 20t and Peter walks 4t. The combined distance covered by both must equal the remaining distance of Peter. So, 20t + 4t = 4.5 => t = 4.5/24 = 3/16 hours.<BR>\n" );
document.write( "5. **Distance walked by Reeta after hopping off:** 4 km/h * (3/16) hours = 0.75 km<BR>\n" );
document.write( "6. **Distance from school when siblings meet Reeta:** 2.5 km + 0.75 km = 3.25 km\r<BR>\n" );
document.write( "\n" );
document.write( "**d) Thursday:**\r<BR>\n" );
document.write( "\n" );
document.write( "1. Let 'x' be the distance from school where Nikita is dropped off.<BR>\n" );
document.write( "2. Time taken by Nikita to walk home: (5-x) / 4<BR>\n" );
document.write( "3. Time taken by Peter to drop Nikita and return to collect Reeta: 2x / 20 = x/10<BR>\n" );
document.write( "4. Reeta walks (5-x) km. Time taken by Reeta to walk the remaining distance= (5-x)/4<BR>\n" );
document.write( "5. Peter and Reeta cycle the remaining distance. The remaining distance is 5-x km. The time taken by Peter and Reeta to cycle = (5-x)/20<BR>\n" );
document.write( "6. Since all arrive home at the same time: (5-x)/4 = x/10 + (5-x)/20<BR>\n" );
document.write( "7. Multiplying by 20, we get: 5(5-x) = 2x + (5-x) => 25 - 5x = x + 5 => 20 = 6x => x = 10/3 km = 3.33 km\r<BR>\n" );
document.write( "\n" );
document.write( "Drop-off and pick-up points are 3.33 km from school.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );