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## Question

Thanks to my friend who I stole this from...(oh well, he will never know ;P)

A commutator commutes to his group at work and back to his community locomotive station daily, arriving at 18:23. His conjugate drives from home to pick him up. Like all conjugates, they are very precise, and arrive precisely as the train arrives. One day, the commutator arrives at 16:23 due to an early release day. Since he did not want to interrupt his conjugate's train of thought, he simply started walking home along the route that which they traverse daily. The conjugate pairs meet along the path, and immediately head back home. They arrive home 23 minutes earlier than usual. How many minutes did the commutator walk before he was picked up by his conjugate?

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an hour?

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1hr, 48mins and 30 seconds?

Well if they arrive home 23 mins earlier than normal, the conjugate has driven 23 mins less.

Which means 11.5 mins there and back. So instead of meeting the guy at 18.23 he meets him at 18.11 and 30 seconds, which is 1hr, 48 mins and 30 seconds after 16.23.

Edited by starfish
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Not enough information? Think about it. There is enough information to tell that the conjugate picked him up sometime after 18:00, but before 18:23. However to know how the time splits between his walking travels and his conjugates mode of transportation, you would first need to know their respective speeds. If both were traveling the same speed then I could confidently agree with the above poster, but such is not the case.

Edited by Austin CG
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Not enough information? Think about it. There is enough information to tell that the conjugate picked him up sometime after 18:00, but before 18:23. However to know how the time splits between his walking travels and his conjugates mode of transportation, you would first need to know their respective speeds. If both were traveling the same speed then I could confidently agree with the above poster, but such is not the case.

No, Starfish is correct (nice job, btw!). You don't need to know speeds. The way I look at this problem is in terms of time-distances (such as light-years), and then all you need are times. Thanks guys!

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I wish my conjugate were so precise. I'll have to get her a better watch. Also instead of her name, I'll just start saying, "Conjugate, you must be more precise. I am wasting time on my commutations."

This is apparently the best I can do in my first post as an advanced member.

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No, Starfish is correct (nice job, btw!). You don't need to know speeds. The way I look at this problem is in terms of time-distances (such as light-years), and then all you need are times. Thanks guys!

I'm having trouble understanding how to arrive at the solution, would someone indulge me?

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Ok, so we know the conjugate arrived home 23 mins earlier than normal.

So think of the conjugates return journey like this:

Home ->--------------------------------------> TRAIN STATION

Home <---------------------------------------<- TRAIN STATION

Now, since he travelled 23 mins less than normal, we can presume he drove only to X, where he met the guy and back.

Home ->------------->X ->……….11.5mins...........-> TRAIN STATION

Home <--------------<- X<-……..11.5mins……......<- TRAIN STATION

As the conjugate would have been at the train station at 18.23, he must have been at X 11.5 mins earlier than this, i.e at 18.11 and 30 seconds.

We know the guy walked until he met the conjugate. Therefore he was walking from 16.23 until 18.11 and 30 seconds, which is 1 hr 48 mins and 30 seconds.

I'm not the best at explaining things......

Edited by starfish
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Ok, so we know the conjugate arrived home 23 mins earlier than normal.

So think of the conjugates return journey like this:

Home ->--------------------------------------> TRAIN STATION

Home <---------------------------------------<- TRAIN STATION

Now, since he travelled 23 mins less than normal, we can presume he drove only to X, where he met the guy and back.

Home ->------------->X ->……….11.5mins...........-> TRAIN STATION

Home <--------------<- X<-……..11.5mins……......<- TRAIN STATION

As the conjugate would have been at the train station at 18.23, he must have been at X 11.5 mins earlier than this, i.e at 18.11 and 30 seconds.

We know the guy walked until he met the conjugate. Therefore he was walking from 16.23 until 18.11 and 30 seconds, which is 1 hr 48 mins and 30 seconds.

Ah, very nice. I think I was also confused because I saw Yoruichi-san say you were correct, but I had accidentally opened akaslickster's spoiler thinking it was yours (so I thought the correct answer was exactly 1 hour). Good little puzzle, thanks!

I'm not the best at explaining things......

Don't shortchange yourself, that explanation was pretty darn good

Edited by frotorious

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