Running Distances

This week, I decided to look at a different topic.  As a runner of track and cross country from 1995-1999 I have always appreciated the math involved in calculating distances.  Most running events are measured in meters and tracks are measured in meters. This is a unique and fun math topic that could be used a variety of ways.

First some basic information:

400 meters is one lap on an outdoor track
400 meters=.25 Miles
800 meters=.5 Miles
1600 meters=1 mile
5 Kilometers= 3.125 miles
10 Kilometers=6.25 miles

Some questions:

If a runner ran two track events a 1600 meter race and an 800 meter race, how many miles did the runner run?  The runner ran a total of 1.5 miles.

A runner ran a total of one mile.  If the track events were 400 meters, 800 meters, 1600 meters, 5K, and 10K, what combinations of events could the runner have ran? (The runner could run twice in the same event.)  The runner could have ran the 400 meter race four times.  The runner could have ran two 400 meter races and one 800 meter race.  The runner could have ran two 800 meter races.  The runner could have also ran one 1600 meter race.

A runner ran two laps on an outdoor track.  What percentage of two miles did the runner run? How could that be represented with a fraction?  Two laps is equal to a half mile since each lap is 400 meters and 400 meters is equal to .25 miles.  Two miles would be 8 laps on the outdoor track.  One half mile is 2 laps.  The fraction could be represented by 2/8 or 1/4 or 25%.

A runner was being timed for the 1600 meter race.  Lap one was 80 seconds, lap two was 80 seconds, lap 65 seconds.  The runner crossed the finish line at exactly 4 minutes and 45 seconds.  What was the runners time for lap 4?  The first three added up to 3 minutes 45 seconds, so the last lap must have been exactly 60 seconds.

A runner wants to run a mile in 8 minutes on a track and runs a consistent pace that remains the same.  Lap one takes the runner 2 minutes.  Lap two takes the runner 2 minutes.  Is the runner running a pace to run a mile in 8 minutes on an outdoor track?  Yes.  Four laps of 400 meters each equals a mile (1600 meters)  If the runner ran 4 laps, each lap taking 2 minutes, the runner's mile time would be 8 minutes.

A runner is following a training program that is four days per week.  The weekly goal is to run 20 kilometers per week, without running more than 10 kilometers in any given day.  The runner runs 2 kilometers on day one, 8 kilometers on day two, and 9 kilometers on day.  The runner wants to run 10 kilometers on day 4.  If the runner runs 10 kilometers on day four, how many kilometers did the runner exceed the goal for that week?  The runner ran a total of 29 kilometers that week and exceeded the goal of 20 kilometers by 9 kilometers.

A runner is running a 3200 meter race.  The runner just completed lap number six.  Write a fraction that represents the amount of the race that the runner has completed so far.  3200 meters would be 8 laps.  The runner has completed 6/8 or 3/4 of the race.

A topic like this could also be incorporated into making graphs.  For example you could give students information and ask them to create their own graphs...

Example:  In a track meet, Sally ran a 3200 meter event, a 1600 meter event, and an 800 meter event.  Bob ran a 400 meter event and an 800 meter event.  Jeff ran an 800 meter event and a 1600 meter event.  Make a graph that represents the total distance each runner ran.

Another way to explore the topic:  Ask kids to create:  Give them a broad topic such as You are the coach and have ten team members.  If there was a limit of each member to run in no more than three events and you had two members that only wanted to run one event each...

The events are the 100 meter race, the 200 meter race, 400 meter race, the 800 meter race, the 1600 meter race, and the 3200 meter race.  Do you have enough team members to have two people in each race?  Yes.  There are a total of six events.  You have ten team members.  Ask them to draw out their schedule of what team members are scheduled in each event. Team members could be represented by Member A and Member B (for the team members that only want to run one event) and Members 1-8 who can run up to three events.

Then after this is complete and they have drawn up their schedule, ask a variable question such as "Now Members 1 and 2 ask to be in the 400 meter race."  Can you accommodate their request and still have team members in every event?  If so, how? 

The Team scenario is could be kind of tricky so I would use it if the group was ready for it and walk and talk them through a similar example on a smart board first.  This is a fun topic that could be altered or modified if needed.