I started by running 6.0MPH for 3.5 minutes. Then I walked 3.5MPH for 1 minute. I repeated the running and walking intervals until I had gone 2 miles. After I completed two miles, my walking intervals were for a minute and a half; my running intervals were still for 3.5 minutes.
How long did it take me to do the 5k?
There is more than one way to figure this out. The easiest was to use Excel or other spreadsheet program like Google’s. Simply add up the times and distances until you got close to 3.12 miles, then do a little math to get the last bit.
| distance (miles) | total distance (miles) | time (minutes) | total time (minutes) | |
| run |
0.35 |
0.35 |
3.50 |
3.50 |
| walk |
0.058333 |
0.408333 |
1.00 |
4.50 |
| run |
0.35 |
0.758333 |
3.50 |
8.00 |
| walk |
0.058333 |
0.816667 |
1.00 |
9.00 |
| run |
0.35 |
1.166667 |
3.50 |
12.50 |
| walk |
0.058333 |
1.225 |
1.00 |
13.50 |
| run |
0.35 |
1.575 |
3.50 |
17.00 |
| walk |
0.058333 |
1.633333 |
1.00 |
18.00 |
| run |
0.35 |
1.983333 |
3.50 |
21.50 |
| walk |
0.0875 |
2.070833 |
1.50 |
23.00 |
| run |
0.35 |
2.420833 |
3.50 |
26.50 |
| walk |
0.0875 |
2.508333 |
1.50 |
28.00 |
| run |
0.35 |
2.858333 |
3.50 |
31.50 |
| walk |
0.0875 |
2.945833 |
1.50 |
33.00 |
| run |
0.174167 |
3.12 |
1.74 |
34.74 |
(.174167 miles)/1 * (1 hour)/(6.0 miles) * (60 minutes)/(1 hour)=1.74167 minutes OR 1 minute,44 seconds
TOTAL TIME: 34 minutes, 44 seconds
Here’s how to do it completely mathematically.
For the first 2 miles, I ran 6MPH for 3.5 minutes, and then walked 3.5MPH for one minute. For this problem, one “set” is one interval of running and walking. How many sets did I finish before hitting 2 miles? How long did it take?
(6.0 miles/hour X 3.5 minutes X 1 hour/60 minutes) + (3.5 miles/hour X 1 minute X 1 hour/60 minutes) = .4083 miles
.4083 miles X a < 2 miles
This is how many miles I ran/walked in each set.
Where a is the # of sets.
Solving for a, I got a < 4.89.
I finished at least 4 sets before hitting 2 miles.
.4083 miles X 4 = 1.63 miles
Now for the rest of the 3.12 miles. First, I ran 6MPH for 3.5 minutes, and then walked 3.5MPH for one and a half minutes. How many sets did I finish before hitting the end? How long did it take?
This is how many miles I ran/walked in each set.
(6.0 miles/hour X 3.5 minutes X 1 hour/60 minutes) + (3.5 miles/1 hour X 1.5 minutes X 1 hour/60 minutes) = .4375miles
.4375miles X a < (3.12-1.63) miles
Where a is the # of sets.
Solving for a, I got a < 3.39.
I finished at least 3 sets before finishing the 5k.
.4375 miles X 3 = 1.3125 miles
3.5 minutes + 1.5 minutes) X 3 = 15 minutes
How many miles I do have left?
(3.12 – 1.63 – 1.3125)miles = .17416 miles
Since I can run .35 miles during an interval of running, then this little bit was completed with just running. How long did that take?
.17416 miles X 1 hour/6.0 miles X 60 minutes/1 hour = 1.7416 minutes OR 1 minute,44 seconds
TOTAL TIME:
(18 + 15 + 1.74) minutes = 34.74 minutes OR 34 minutes,44 seconds