Practice Problem 3

The record for the Kentucky Derby is held by Secretariat, who ran the 10 furlongs in 1 minute, 59.4 seconds. Calculate his average speed in miles per hour.

Solution

The key to this calculation is keeping track of the units used to express the dimensions of the problem. The problem gives the distance for the Kentucky Derby in furlongs and the length of the race in minutes and seconds. It then asks us to convert these data into units of miles and hours. We can start by looking up the definition of a furlong: 1/8 mile. Two unit factors can be constructed from the definition of a furlong. One describes the number of furlongs per mile. The other tells us the number of miles in a furlong.

If we multiply 10 furlongs by the appropriate unit factor, the units of furlongs cancel and the distance comes out in the desired units, miles.

(There are an endless number of significant figures in this result because none of the quantities in this calculation are measurements. The distance of the Kentucky Derby is defined as 10 furlongs, and a furlong is defined as 1/8 of a mile.) To complete this problem we must convert 1 minute, 59.4 seconds into units of hours. We might start by calculating the total number of seconds.

We can then use the appropriate unit factors to convert seconds into minutes and minutes into hours.

To calculate the average speed in miles per hour we divide the distance traveled in miles by the time it took in hours.

The answer is 37.68 mi/h.