Roller Coaster Math

Sunday, February 23, 2014 3:22 PM

A new Six Flags park is planning to open 3 new roller coasters. They test the prototypes for the rides on 3 congruent circular tracks each 5000 meters long. The coasters travel 44, 48, and 50 meters per second, and the park decides to stop testing once all the coasters reach the same position on the track. Given that all 3 coasters start at the same position, how long will Six Flags have to keep testing?

Sunday, February 23, 2014 4:44 PM

who's the manufacturer?

Sunday, February 23, 2014 6:37 PM

Do the riders have flash pass? Because if they don't Six Flags is going to intentionally slow down the loading to artificially increase wait times.

Sunday, February 23, 2014 6:49 PM

Fine. A new Six Flags park gets three coasters, and Michigan's Adventure gets nothing again.

Sunday, February 23, 2014 7:20 PM

They will stop immediately after they crest the lifthill because Six Flags will set the trim breaks to slow the trains to 30 meters per second, thereby never giving them the chance to pull away from each other in the first place.

Sunday, February 23, 2014 7:42 PM

Let t = the time elapsed since testing began.

Since the tracks are closed loops we are really looking for the displacement from the beginning. We could set up a modular arithmetic problem.

The displacement of the coaster on track A is 44t (mod5000). Track B is 48t(mod5000). Track C is 50t(mod5000). Set up equations for A = B, B = C, and A = C.

The solution to A = B is t = 1250n where n = 1, 2, 3, ....

The solution to A = C is t = 2500n where n = 1, 2, 3, ....

The solution to B = C is t = 1250n where n = 1, 2, 3, ...

Each equation shares a common solution when t = 2500 s or 41 min and 40 s. Interestingly enough the coaster cars will end up at the starting point of testing.

Sunday, February 23, 2014 8:19 PM

And with that, I hope you thank mulfinator for doing your homework for you. ;)

Sunday, February 23, 2014 8:32 PM

I'll thank him. I have no idea what all that means. (He lost me at "let t = the time elapsed".....)

Sunday, February 23, 2014 10:05 PM

If only I got homework about roller coasters...

(Your solution is correct, BTW)

Last edited by blasterboy6500, Sunday, February 23, 2014 10:06 PM
Sunday, February 23, 2014 11:08 PM

El Toro's train will meet Rolling Thunder's train in 52.3 seconds.

Monday, February 24, 2014 9:37 PM

Raises hand. Testing is only accurate if there are no break downs. But, knowing six flags, one of the 3 is bound to be experiencing delays. If you would like to recalculate please do so now. We are not sure when or if coaster two will will retest, but we thank you for waiting. Enjoy the rest of your day in the six flags testing forum. LOL!!

Tuesday, February 25, 2014 9:41 AM

The answer is D.) Michigan's Adventure.

Tuesday, February 25, 2014 10:03 AM

I think the bigger question is whether or not Cedar Fair is going to buy this park just to shut it down and eliminate competition with a flagship park.

Last edited by sirloindude, Tuesday, February 25, 2014 10:03 AM
Tuesday, February 25, 2014 4:03 PM

Screw those Chinese and their Remainder Theorem.

Last edited by ApolloAndy, Tuesday, February 25, 2014 4:04 PM
Tuesday, February 25, 2014 6:45 PM

ApolloAndy said:

Screw those Chinese and their Remainder Theorem.

I knew number theory would come in handy at some point in my life. I just didn't realize it would be on Coasterbuzz.

Wednesday, February 26, 2014 11:01 AM

Did anybody do the real math on that problem? At those speeds, Assuming sustained speeds as described and conventional steel coaster hardware, they'll have to stop to change wheels before they complete the first circuit.

--Dave Althoff, Jr.

Friday, February 28, 2014 12:30 AM

What happens of the train dosn't clear the lift hill?

Friday, February 28, 2014 12:43 AM

You're all wrong. The green train only makes it 1/8th of the way around the circle before ramping off into the lake. The answer is, the solution does not exist.

Last edited by D_vo, Friday, February 28, 2014 12:43 AM

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