Team Building Exercise

Joe and Shmo are building a bike. If they work together, it takes them 4 hours to finish. However... if Joe builds half of it alone, and Shmo joins in for the other half it takes a total of 5 hours to build.

How long would it take Shmo to build the bike alone?

@joe-shmo
12 hours

@bigdoggproblem said
@joe-shmo
12 hours

Correct!

@joe-shmo said
Joe and Shmo are building a bike. If they work together, it takes them 4 hours to finish. However... if Joe builds half of it alone, and Shmo joins in for the other half it takes a total of 5 hours to build.

How long would it take Shmo to build the bike alone?

I'm coming to the conclusion that my brain must be too addled with age and alcohol to work out your (excellent) puzzles!!
There's obviously something wrong with my logic here.Can you put me right? :-
If it takes Joe and Shmo 4 hrs to finish in 1 hour they have built 1/4 of the bike so Joe has built 1/8th of it.
Therefore in 4 hours Joe has built 4/8th's or half the bike.
But we are told that in five hours Smo joins and the bike is finished.
So,if in 5 hrs Joe has built 5/8th's of the bike the other 3/8ths must have been built by shmo for the bike to be finished.
If shmo can build 3/8th's in 1 hour he can build 1/8th in 20 minutes,so if he is on his own he can build 8/8th's in 160 minutes or 2hrs 40 minutes.
Not correct obviously.
As for your train puzzzle. All I know for sure is that when the front of the trains get to Joe the speed is 50mps(combined speed of both trains)
As no one else seems to have had a go I can only conclude it is beyond the ability of the others as well,although Mr Tracks hasn't posted for a while.

@venda said
I'm coming to the conclusion that my brain must be too addled with age and alcohol to work out your (excellent) puzzles!!
There's obviously something wrong with my logic here.Can you put me right? :-
If it takes Joe and Shmo 4 hrs to finish in 1 hour they have built 1/4 of the bike so Joe has built 1/8th of it.
Therefore in 4 hours Joe has built 4/8th's or half the bike.
Bu ...[text shortened]... onclude it is beyond the ability of the others as well,although Mr Tracks hasn't posted for a while.

"I'm coming to the conclusion that my brain must be too addled with age and alcohol to work out your (excellent) puzzles!!"

They aren't my puzzles! I'm just a messenger. These are just some highlight reel from the puzzles I've solved on "Brilliant.org" that don't require pictures to explain the problem setup.

As for the problem, I have to stop you on the first line:

If it takes Joe and Shmo 4 hrs to finish in 1 hour they have built 1/4 of the bike so Joe has built 1/8th of it.

They can do work at different rates.

Let "J" be the rate Joe works ( fraction of bike built per hr ), and "S" be the rate Shmo works.

The first equation is then :

4*J + 4*S = 1

in words 4 hrs at Joe's rate and 4 hrs at Shmo's rate builds them 1 bike.

I'll let you try and come up with the rest ( the next equation ) yourself, before I finish.

@venda said
I'm coming to the conclusion that my brain must be too addled with age and alcohol to work out your (excellent) puzzles!!
There's obviously something wrong with my logic here.Can you put me right? :-
If it takes Joe and Shmo 4 hrs to finish in 1 hour they have built 1/4 of the bike so Joe has built 1/8th of it.
Therefore in 4 hours Joe has built 4/8th's or half the bike.
Bu ...[text shortened]... onclude it is beyond the ability of the others as well,although Mr Tracks hasn't posted for a while.

"As no one else seems to have had a go I can only conclude it is beyond the ability of the others as well,although Mr Tracks hasn't posted for a while."

Everyone has there own puzzles types. Maybe the flavor isn't right.

@joe-shmo said
"I'm coming to the conclusion that my brain must be too addled with age and alcohol to work out your (excellent) puzzles!!"

They aren't my puzzles! I'm just a messenger. These are just some highlight reel from the puzzles I've solved on "Brilliant.org" that don't require pictures to explain the problem setup.

As for the problem, I have to stop you on the first line: ...[text shortened]... bike.

I'll let you try and come up with the rest ( the next equation ) yourself, before I finish.

Ok thanks.
Didn't consider that but I knew something was amiss.
If I were Joe, and Shmo wasn't pulling his weight I'd sack him and build the damn thing myself!!
I'll get to it later.
I'm busy preparing all my sheets for the new crown bowling season which starts soon at the moment ,plus trying to keep up with chess games!!
I do all the stats etc for all the players in the club besides preparing selection notices and availability sheets for the members to fill in.

@venda said
Ok thanks.
Didn't consider that but I knew something was amiss.
If I were Joe, and Shmo wasn't pulling his weight I'd sack him and build the damn thing myself!!
I'll get to it later.
I'm busy preparing all my sheets for the new crown bowling season which starts soon at the moment ,plus trying to keep up with chess games!!
I do all the stats etc for all the players in the club besides preparing selection notices and availability sheets for the members to fill in.

Have Fun!

@venda said

As no one else seems to have had a go I can only conclude it is beyond the ability of the others as well,although Mr Tracks hasn't posted for a while.

Hi Venda and Joe

First, thanks for your interesting and challenging puzzles. When I see them, they certainly exercise my brain, and I enjoy solving them (if I manage to!)

I am not a regular on this site anymore, have been frustrated by being constantly harangued by a pair of posters on the General Forum who seem to be laying the whole of the RHP forums to waste wherever they tread. So be it.

Your contributions to this puzzle forum are extremely interesting, and I will pop in to take a look every couple of weeks.

Thanks for your time and honest, supportive postings.

If only all of the forums would do the same!

@Blood-On-The-Tracks

This is easily the best forum on RHP right now.

Not full of mentally ill people and manufactured drama.

@joe-shmo said
Joe and Shmo are building a bike. If they work together, it takes them 4 hours to finish. However... if Joe builds half of it alone, and Shmo joins in for the other half it takes a total of 5 hours to build.

How long would it take Shmo to build the bike alone?

Sorry to be such a numpty, but I can't seem to get the right answer(12)
4J + 4S=1
5J +2.5S=1
Multiplying out to eliminate J you get
20J +20S =5
20J +10S =4
10S =1
So S =10 hrs
I suppose my second equation is incorrect?

@blood-on-the-tracks said
Hi Venda and Joe

First, thanks for your interesting and challenging puzzles. When I see them, they certainly exercise my brain, and I enjoy solving them (if I manage to!)

I am not a regular on this site anymore, have been frustrated by being constantly harangued by a pair of posters on the General Forum who seem to be laying the whole of the RHP forums to w ...[text shortened]... hanks for your time and honest, supportive postings.

If only all of the forums would do the same!

Nice to hear from you again
I think I know what you mean about the forum trolls.
I don't go on the general forum but I do go on the site ideas and clan forums and post if I've something to say.
I did get an encouraging reply when I suggested 2 of the people I think you are referring to should tone it down a bit.
I haven't really looked since.Been too busy with the puzzles,chess games and other aspects of my otherwise mundane life!!

@venda said
Sorry to be such a numpty, but I can't seem to get the right answer(12)
4J + 4S=1
5J +2.5S=1
Multiplying out to eliminate J you get
20J +20S =5
20J +10S =4
10S =1
So S =10 hrs
I suppose my second equation is incorrect?

Yes, it is. That's the equation you would use, if Shmo worked half as long as Joe, but the problem statement indicates that Joe builds half of the bike.

You'll need to solve for the two times.

@joe-shmo said
Joe and Shmo are building a bike. If they work together, it takes them 4 hours to finish. However... if Joe builds half of it alone, and Shmo joins in for the other half it takes a total of 5 hours to build.

How long would it take Shmo to build the bike alone?

Even knowing the answer,I still can't form the equations in my head.
Perhaps I ought to log in to the website you mentioned and try and sharpen up my skills!!

@venda

Hi Venda, maybe this will help. I 'did it' a different way, but I think I can help you through Joe's explanation.

From the 2nd scenario, where Joe starts then his mate joins in, take the last bit first. They finish half the bike. From the first scenario, it takes them 4 hrs to build a bike, so this half bike takes 2 hrs. As the whole process in scenario 2 is 5 hrs, it means Joe builds half a bike in 3 hrs (5-2)

So, Joe takes 3 x 2, =6 hours to build a bike on his own. By Joe's method, that means J= 1/6 (the number of bikes Joe builds in an hour)

Nearly there. Put that into the first equation (4J + 4S =1), and we get 4/6 + 4S = 1, so 4S = 1/3, so S=1/12.

S is the number of bikes Shmo makes in an hour, so it takes him 12 hrs to make a bike on his own.

As you say, if I were Joe I would put him in the queue for the teddy bear in the fairground problem, or even worse, get him shaking the million dice to try to get no even number! (Other recent puzzles)

Hope that helps