2410 /www/nrich/html/content/id/2410/ 1 2013-01-04T16:41:23 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> <p> I walk to the bike shop at 3 miles per hour and cycle back along the same route at 12 miles per hour. What is my average speed in miles per hour, for the time I am actually travelling on the route? </p> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><p>Suppose the distance to and from the bike shop is $x$ miles.<br></br> Then the time taken on the journey there is $\frac{x}{3}$ hours, and the time taken on the journey back is $\frac{x}{12}$ hours.<br></br> <br></br> So altogether a distance of $2x$<comment>#perl sub="HTML::TeX" mode="" arg=" Let the distance to the bike shop be \$ d \$ miles. Then the time going is \$ \frac{1}{3}d \$ hours and the time returning \$ \frac{1}{12}d \$ hours. The total time travelling is therefore \$ \frac{1}{3}d + \frac{1}{12}d = \frac{5}{12}d\$ and the total distance is\$ 2d \$ miles giving the average speed as \$ \frac {2d}{\frac{5d}{12}} = \frac{24}{5} \$ miles per hour." </comment>miles is travelled in $\frac{x}{3} + \frac{x}{12} = \frac{5x}{12}$ hours.<br></br> <br></br> So the average speed is $2x \div \frac{5x}{12} = 4.8$ miles per hour.</p></mdoxml> 2 3 0 0 1 0 0 Weekly Problem 8 - 2013 Measures and Mensuration Speed