Explain how you would determine who is fastest (Grade 6, no calculator!): A: 35 laps in 84 min B: 42 laps in 96.6 min C: 38 laps in 102.6 min #MTBoS #ITeachMath My method seems a bit convoluted so I wanted to see if anyone can come with something simpler! 😀 - ThreadSky

bobsonwong.com • 49 days ago

Explain how you would determine who is fastest (Grade 6, no calculator!):
A: 35 laps in 84 min
B: 42 laps in 96.6 min
C: 38 laps in 102.6 min
#MTBoS #ITeachMath

My method seems a bit convoluted so I wanted to see if anyone can come with something simpler! 😀

Comments

johngolden.bsky.social•49 days ago

A>C bc almost same in way more time. A&B... both multiples of 7, so 35/5 in 84/5 ~17 min, 42/6 in 96/6 ~ 16 min. B is fastest. Pretty close.

tcorica.bsky.social•49 days ago

Just as others have said but also: I note that 35 and 42 are both divisible by 7, so I see a ratio of 5 to 6. B gets 20% more laps done; let's see if it takes him more or less than 20% more time. 20% of 84 is 16.8 or about 100 min, which is more than B took, so B is faster. But.... 1/2

tcorica.bsky.social•49 days ago

"Faster" to us means "faster avg rate". Since they are running different distances, though, the avg might not quite tell us who is "faster". A sprinter might run 1 lap in 1 min, but it doesn't seem fair to compare. In your example, the fastest is also running the farthest, so it's moot. 2/2

bobsonwong.com•49 days ago

Thank you for responding! 😀

germinalmaths.bsky.social•49 days ago

Compare times for 42 laps.
C must take > 102.6 minutes which, in turn, is longer than the 96.6 minutes taken by B.
A must travel a further 7 laps, one-fifth more than 35 laps. One-fifth is two-tenths, so this would take 84 + 2 x 8.4 = 100.8 minutes, also longer than B.

B is fastest over 42 laps.

bethhentges.bsky.social•49 days ago

It can’t be C because C did fewer laps and took a longer time than B.

Then:
35=7(5)
42=7(6)

Multiply both numbers in A by 6, and multiply both numbers in B by 5. Then compare.

benjamindickman.bsky.social•49 days ago

A. 84/35 cancel 7s 12/5 = 2.4 minutes on each lap

B. 7 more laps at same speed would take 16.8 more minutes; this is faster!

C. 3 more laps at A speed would take 7.2 minutes; this is way slower

B is fastest

benjamindickman.bsky.social•49 days ago

C is way slower so it's between:

A: 35 laps in 84 min
B: 42 laps in 96.6 min

35/84 = 5/12 = 40/96
an extra 2 laps in 0.6 minutes is very fast, B wins

bobsonwong.com•49 days ago

Ooh, I like this explanation! :)

benjamindickman.bsky.social•49 days ago

bless 🙏🏻 it's all yours!

sharonvestal.bsky.social•49 days ago

I tried to think about how many laps they could each do in 100 minutes. I estimated that B could do 2 more laps, so between 43 & 44 laps in 100 minutes. Then I estimated that A was taking about 2.5 minutes per lap so they could do about 6 more, which means 41 laps. Therefore, B is fastest.

jclevelandtran.com•49 days ago

Well, B is clearly faster than C, so I only need to compare A and B. A is 5 laps in 12 min. B is 7 more laps than A, so it’s doing 2 bonus laps in .6 min. That seems fast, so B it is.

bobsonwong.com•49 days ago

I immediately ruled out C too, but how would you explain it to a 6th grader?

jclevelandtran.com•49 days ago

Well, it’s more laps in fewer minutes. (I don’t have much experience with 6th graders but that seems reasonable.)

bobsonwong.com•49 days ago

Yes, that was essentially what I said as well. :)

triangleman.bsky.social•49 days ago

Yes! More laps in fewer minutes. And then B does 7 more laps than A in about 12 extra minutes, which is less than two minutes per lap, a speed faster than any of them averages. So B has fastest average speed.

triangleman.bsky.social•49 days ago

And yes these are accessible to sixth graders, so long as they aren’t frightened off by the needless .6 minutes

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