More Math for Fun

[Debater Slayer]

As part of an hour-long workout, Joe starts by clapping and doing a push-up at the same time. Afterward, he does a push-up every 15 seconds and claps every 20 seconds. How many times will Joe clap and do a push-up at the same time during his workout?

As always, please use spoilers for your answers!

 

[beenherebeforeagain]

As part of an hour-long workout, Joe starts by clapping and doing a push-up at the same time. Afterward, he does a push-up every 15 seconds and claps every 20 seconds. How many times will Joe clap and do a push-up at the same time during his workout?

As always, please use spoilers for your answers!

Is that all that he does in his workout? Or does he do other things than clapping and pushups? No jumping jacks? No leg lifts?

 

[Debater Slayer]

Is that all that he does in his workout? Or does he do other things than clapping and pushups? No jumping jacks? No leg lifts?

Nothing else. The question is focused on the push-ups and clapping only.

 

[Exaltist Ethan]

Spoiler

Sixty times. Once a minute, every minute for sixty minutes in an hour.

 

[ChristineM]

Spoiler: Purely a guess

Somewhere around 60 (or possibly 61)

 

[Viker]

You're gonna make my head implode, yanno?

 

[It Aint Necessarily So]

Spoiler

61, unless you want to disqualify the last act by saying that it occurred at the start of the second hour, in which case it's 60

 

[Subduction Zone]

I need more details. How is he doing this? Okay, I understand clapping pushups. But what is he doing when the clap does not occur during the push up?

 

[Subduction Zone]

While I am waiting for details:

Spoiler

60

 

[Debater Slayer]

I need more details. How is he doing this? Okay, I understand clapping pushups. But what is he doing when the clap does not occur during the push up?

Such problems usually assume ideal conditions, so he doesn't fail any claps.

 

[icehorse]

As part of an hour-long workout, Joe starts by clapping and doing a push-up at the same time. Afterward, he does a push-up every 15 seconds and claps every 20 seconds. How many times will Joe clap and do a push-up at the same time during his workout?

As always, please use spoilers for your answers!

I suspect you mean "during the workout" or "thereafter during the workout" or some such?

I didn't do the math, but I can tell you that this appears to be the sort of problem that computer programmers might agree can likely cause "off by 1" errors

 

[Debater Slayer]

I suspect you mean "during the workout" or "thereafter during the workout" or some such?

I didn't do the math, but I can tell you that this appears to be the sort of problem that computer programmers might agree can likely cause "off by 1" errors

Yes, during the workout. "Afterward" here means "after the very first instance of doing a push-up and clapping."

 

[idea]

Spoiler: Spoiler

60

 

[Alien826]

If he's anything like me, he gets tired after five pushups. then fumbles the next one and lands on his nose. In hospital he has time to think about it and decides to do the clapping standing up next time. He can't remember how many times he did the claps and pushups, so the answer is not known.

 

[Kenny]

As part of an hour-long workout, Joe starts by clapping and doing a push-up at the same time. Afterward, he does a push-up every 15 seconds and claps every 20 seconds. How many times will Joe clap and do a push-up at the same time during his workout?

As always, please use spoilers for your answers!

Spoiler: how many times?

60 - Both of them match on the minute... there is 60 minutes in an hour - thus 60

 

[Brickjectivity]

Spoiler: workout

Initially one clap and one pushup, and then every 15 seconds a pushup with a clap every 20 seconds. His workout ends in exactly 3600 seconds, so the last clap and pushup within that time is what we will count up to. We can assume that the first clap and pushup take part of the first second or a whole second, which leaves 3599 seconds for the rest of the workout.


Pushups: 1 + (3599 - 3599 mod 15)/15 = 240
Claps: 1 + (3599 - 3599 mod 20)/20 = 180

I tried to find a name for the above operation of f() = (M - M mod N)/N. I couldn't find a name for it. It means "Count as many as will fit and round off."

 

[Shadow Wolf]

I need more details. How is he doing this? Okay, I understand clapping pushups. But what is he doing when the clap does not occur during the push up?

If little Johnny or whatever his name is DARES to deviate from the MATH amd the FORMULA the answers gonna be a 0 because his hands are getting shattered for making me do all that whole lot of little bit of thinking for nothing!

 

[Subduction Zone]

If little Johnny or whatever his name is DARES to deviate from the MATH amd the FORMULA the answers gonna be a 0 because his hands are getting shattered for making me do all that whole lot of little bit of thinking for nothing!

The wording was a bit vague so I just did it in my head. No pen and paper needed.

That reminds me of when I was tutoring a nephew in math. His work was in pencil, and very neat. He erased any errors. I had to convince him not to do that. I could see where he screwed up, but I could not understand his reasoning. I said that I wanted it messy. In pen. If he made an error just put a line through it. That made my job much easier because I could see when and where he got off track. When you just look at something and all you can say is "that's wrong" a person is not going to learn much. But if you look at it and said "that's wrong and here is where and why you went wrong then it is much easier for them to learn from their errors.

 

[beenherebeforeagain]

Spoiler

Because the person already did one combination, and you are interested in the rest of the hour's workout, I will hazard 59, since he's already done one.

 

[Daemon Sophic]

Yes, during the workout. "Afterward" here means "after the very first instance of doing a push-up and clapping."

OK. Maybe you're British or something ....but until this clarification, there was no way to understand the given parameters of your OP.

So, for clarity, he does 1 clap/push-up; then after that one occurrence, he claps every 20 seconds, and does a push-up every 15 seconds over the next 1 hour. And you're asking, over the length of his "work-out", how many times do his push-ups and claps coincide?

Spoiler: Mental and physical fitness

Every 60 seconds, on the 60-second-point, his push-ups and claps coincide. Also, at that moment, the timer on both activities resets to zero, and we start over. So he gets a coincidence at the end of minute #1, and at the end of every minute including the end of minute #60.

Thus 60 total PLUS the first clap/push-up.
Therefore the final score is 61 clap/push-ups.

PS - Don't Skip Leg Days​