The table shows the distance in miles and your average speed for each portion of the sprint triathlon, where r is your average speed of swimming. We will use the formula for time in order to find the function that models the total time, T, in hours it takes to complete the race.
Time=Distance/Speed
Let's use this formula and divide each distance by speed in each row in the table.
Distance (miles)
Speed (mph)
Time (hours)
Swimming
0.5
r
0.5/r
Bicycling
22
15r
22/15r
Running
6
r+5
6/r+5
The sum of the expressions from the last column in the table models the total time it takes to complete the race.
T=0.5/r+22/15r+6/r+5
b We are asked to find the total time of the race if your average speed of swimming is 2 miles per hour. Let's substitute 2 for r into the equation from Part A and find the total time T.
