2167 /www/nrich/html/content/04/weekly/prob7/ 1 2010-11-14T17:47:22 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p>A pencil AB lying on a table is given a half turn about the end B (so that A moves to A*) and then a half turn about A* (so that B moves to B*). The point C on the pencil is one third of the way from A to B.</p> <p style="text-align: center;"><mdo:image alt="Weekly Problem 2" height="61" src="2-1.png" width="151"></mdo:image></p> <p>What is the ratio of the total distances moved by A and by C?</p> <p> </p> <p>If you liked this problem, <a href="http://nrich.maths.org/6468">here is an NRICH task</a> which challenges you to use similar mathematical ideas.</p></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p>Ans 1:1</p> <p>Let AB have length 3r. The distance moved by A is then the circumference of a semicircle radius 3r (3$\pi$r). C moves along a circle of radius 2r (2$\pi$r), followed by a semicircle of radius r ($\pi$r). The total distance moved by C is therefore also 3$\pi$r. </p> <br></br></mdoxml> 2 3 0 0 0 0 0 Weekly Problem 37 - 2011 Secondary Mapping Document Fractions, decimals, percentages and ratio