We began this lesson wondering who, on average, was faster: Usain Bolt, in a competitive 100-yard foot race, or Marcel Hug, in a competitive 26-mile wheelchair race. You might expect Bolt to be faster; after all, he only had to keep it up for 10 seconds! Hug, by contrast, had to push himself and his wheelchair for more than an hour. But things don't always turn out the way we expect. Let's see what the numbers have to say. Usain Bolt's average speed is average speed distance traveled time taken Marcel Hug's average speed is average speed 20.2 mph = ? miles hour In 20.2 m S Hug's number is nearly twice as large as Bolt's. Did Hug go twice as fast as Bolt, on average? It's hard to say, until you know how to convert between mph and m/s. 20.2 mph = 20.2 = 10.2 m S First, we have the lengths. The conversion factor is 1 miles = 1,609 meters. 1609 meters 1 mile distance traveled time taken = 20.2 1 mile 1609 meters miles hour we want to replace miles with meters (in the top part of the fraction, that is, in the numerator). So we want the conversion factor to have miles in the bottom part of the fraction (that is, in the denominator). 1,609 meters 1 mile = 1. x ?. 100 meters 9.81 seconds 26.2 miles 1.30 hours = 20.2 mph. We can multiply anything by 1! So let's use the version of 1 that makes miles disappear and leaves us with meters in its place. miles hour some