Winner! Make that winners!

Katherine — Sat, 11 Jul 2009 03:22:19 +0000

There were only two people brave enough to solve the problem and for their efforts, they will BOTH get a $10 gift certificate. Congratulations to Ethan (http://www.twitter.com/ethanullman) and Jessica (http://www.twitter.com/TRC_Jessica).

Treadmill and Math!: Answer!

Katherine — Sat, 11 Jul 2009 03:19:30 +0000

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

Treadmill and Math!

Katherine — Thu, 09 Jul 2009 11:42:52 +0000

Edit: I will randomly select from the comments on this post with the correct answers. The winner will get a $10 gift certificate to Amazon. Deadline is July 10^th at 7PM, EDT.

This morning, I ran a 5k (3.12 miles) on the treadmill. I did really good! I alternated between running and walking.

I thought this would be a fun math problem! Yay for math!

How long did it take me to do the 5k?

Here is the tinyURL to this post: http://tinyurl.com/ltyzsx
See if your friends can answer the question! I will have all comments hidden until I reveal the answer tomorrow. Good luck!

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Winner! Make that winners!

Treadmill and Math!: Answer!

Treadmill and Math!