Friday, June 14, 2013

Who is Faster?

My kids love racing each other: on foot, bikes, roller skates or scooter.
They also love arguing: you are older, so you have to give me a headstart, your legs are longer, but you are lighter.
Well, my son is 13 and is 6'8", my daughter is 10 and is 4'9".
How can I help them decide who is faster, factoring their age and size?

Image by Shanti Knapp, distributed under CCL.

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.


anne-marie said...

let's suppose it's a linear function.
The slope would be m= 6.8-4.9/ (13-10)=1.9/3
The point-slope form of the linear function is
y-6.6=1.9/3 (x-13)
Then we could develop and rewrite the equation in slope intercept form y= m x+b

Maria said...

Sorry all, I made a mistake.
Of course my 13-year old is still not 6'8" but 5'8", just a bit taller than I. But I am afraid 6'8" is yet to come:)

Jerome said...

No matter what the contest, as long as it is timed, lends itsef to math solutions.

Suppose the race is a 100 yard dash. Take each kid out separately and time the time to run 100 yards. Suppose it takes your daughter takes 25 seconds. Your son takes 20 seconds. That means that each one goes

Son: 100 yards / 20 sec = 5 yards a second
Daughter: 100 yards / 25 sec = 4 yards a second

Now the question is where do you place your daughter so she will finish at the same time as your son?

In 20 seconds she will cover 80 yards, so you give her a 20 yard head start. Actually that will encourage both of them to get better.

As she gets better, reduce how much of a head start she gets. As he gets better, increase her head start.

If the game has no time involved like horse, you have to keep track of how many times each has to shoot before they get a basket. You can use the same sort of ratio to figure out how many letters you give the better shooter.

Handicapping in Golf is a tremendous problem. I think if I were you, I would hope that my kids never ask you to do it. On the other hand, why not. It is a math problem after all. Here's something to read about it.

It won't stop the arguments, but it might add interest.

Anonymous said...


Siblings love to compete over who is faster, stronger, better. I remember doing so with my siblings.
For your kids:
1) One way you could level the playing field as to whom is faster would be to look at each of their stride lengths and handicap your son accordingly. Natural stride length has been estimated as 41% of height. For your kids (5'8" (68") and 4'9" (57"), your son's stride would be approximately 1.2 x as long as your daughter's. If your kids run the same distance in a time of t-s (son) and t-d (daughter), you can multiple your son's time by 1.2 sec and see who won then. (note: bigger stride doesn't always equate to faster speeds; elite runners on long races for example, have smaller strides than recreational runners, and instead have a much higher cadence.)
2) Instead of using height, you could handicap your son by age (13/10) and multiple his time by 1.2 sec.
3) For a bicycle race, you could look at wheel circumference and handicap your son if his bike is bigger, though both your children might be big enough that they have adult size bikes with 27" diameter wheels, or you could handicap him again based on his height.
4) You could emphasize to your kids that each of them has strengths - I am sure your daughter is better at some things than her older brother -- and that your son may be able to jump higher, run faster, she can do these other things better (including, I'd suspect an obstacle course where smaller height and size are more advantageous than being bigger.)
5) You could also tell you kids that no matter who is faster, stronger, that there are animals out there who are even faster or stronger than them relative to body size. Some people have estimated that the faster animal on earth relative to size is the tiger beetle, which can travel 125 x its body length in one second, compared to the fastest human who travels just 7 times its body length in 1 sec ( There is a interesting web site ( which looks at animal speeds relative to height for a number of different land, water, and air animals, and allows the user to enter in a height to get the equivalent speed if the animal was that size.

Maria said...

Wow, what an informative and inspiration answer from Tracy and pretty good answers from Jerome and Anne-Marie. Thank you for all these great math and parenting ideas - I will share them next week in the newsletter.

Many of you told me that it is a hectic time - school graduation, sleep-away camp packing and farewells. Thanks for finding the time to play along among all this. Bring me back some puzzles from your summer travel or camps or impossibility of combining child care, outdoor fun and work. I find it that I get many new ideas when I step away from my regular routine.

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