Order book

View book Table of Contents

Links

Algebra for Athletes.com

6. Speed

This section discusses how speed, distance, and time are related.   Knowing how speed, time and distance are related will help you understand the travel of trains, airplanes, missiles, satellites, and all objects that move. 

In this section we assume that travel stays at a constant speed.  As you know, travel in sports doesnít always stay at a constant speed. Some runners will get tired at the end of a race and slow down.  Other runners will accelerate near the end of a race.  Although this section studies only constant speed, changing speed, or acceleration, will be studied later. 

6.1 The Speed Equation 

Speed, time, and distance is are related by the following equation: 

                                    d =  rt             whered  = distance                                       (6-1)

                                                                        r  = the rate of travel, or speed

                                                                        t  = time

To help remember the equation, it is often referred to as the "dirt" equation from the pronunciation of the variables.  The following problem shows how the equation is used.

Example 6.1:  If a jogger maintains an average speed of 10 mi./hr., how far can she run in a half hour? 

Solution:        For      d =  rt              where             d= distance, in miles

                                                                                    r = the speed =  10 miles/hour

                                                                                    t= time = 1/2  = 0.5 hr.

Then  d = rt = (10 mi./hr.)(0.5 hr.) 

= 5 miles 

The runner will be able to travel 5 miles in a half hour.

Example 6.2:  A cyclist is in a 75-mile race.  The record time for the race is 2 hours 30 minutes (2.5 hours). How fast will his average speed need to be to beat this record?

Solution:  In this problem, we first need to solve the equation for r.

Again, for      d =  rt              where      d = distance = 75 mi.

                                                                   r = speed, in mi./hr.

                                                                    t= time = 2.5 hr. 

We start off by dividing both sides of the equation by r.

After weíve solved for t, we can put the numbers in the equation. 

The cyclist will need to travel at an average speed faster than 30 mi./hr. to beat the record. 

Home