Knightmare Running
Knightmare (one of our fellow puzzlers) has decided to improve his fitness by jogging ... heh heh.
He stands from the couch, dons running gear, and hits the road. Upon approaching a long, familiar railroad bridge, he knows it will take 3 minutes for him to cross. He is 1/4 of the way across when he hears the train whistle behind him. Being familiar with the road, he knows the crossing where the train just whistled, and he knows the speed of the train. He calculates it will take 1 minute for the train to reach the bridge. If he continues forward, he realizes he would be 15 seconds from the end of the bridge when the train stikes him. He also calculates that by turning around and heading back, he will have just enough time to exit the bridge before the train reaches it. His jogging speed is 8 mph ...
What is the speed of the train?
He stands from the couch, dons running gear, and hits the road. Upon approaching a long, familiar railroad bridge, he knows it will take 3 minutes for him to cross. He is 1/4 of the way across when he hears the train whistle behind him. Being familiar with the road, he knows the crossing where the train just whistled, and he knows the speed of the train. He calculates it will take 1 minute for the train to reach the bridge. If he continues forward, he realizes he would be 15 seconds from the end of the bridge when the train stikes him. He also calculates that by turning around and heading back, he will have just enough time to exit the bridge before the train reaches it. His jogging speed is 8 mph ...
What is the speed of the train?
posted by Zaux at
3:53 PM
33 Comments:
It doesn't matter, it was only a nightmare (groan).
If Pequod can carry Knightmare back to the start (1/4) of the track within 1 minute.
And Pequod carries at 8 mph.
Then
8mph*1h/60minutes*1 minute= 8/60 miles
total bridge length = 4*8/60 miles=32/60=16/30
if he is 15 seconds short of the edge if Pequod carries Knightmare forward then he is
15s*8mph*1h/60 minutes*1 minute/ 60 seconds=120/3600 miles=1/30 short of the end
so Pequod travels (total bridge length- 1/4 bridge length- 15s length)=16/30-4/30-1/30=11/30 miles
Time for pequod to travel 11/30 miles=11/30miles/8 mph=11/240h or 11/4 minutes=2.75 minutes
Train is 1 minute to reach tracks so it only has 2.75-1=1.75 minutes
It travels (total bridge length- pequod's 15s length)=16/30-1/30=15/30=1/2 mile
1/2 mile/1.75 minutes*60 minutes/hour=17.14 mph
Answer:
Train travels at 17.14 mph
Cam
You'll be giving Pequod ideas.
This has got to be the most unrealistic situation in the history of puzzles.
I was about to post 13.5 mph, but just saw Cam do it using the data corresponding to Knightmare escaping. I used the data corresponding to him being wiped out 'cos that seemed like more fun. If you could see the scrawl I've made you'd know why I've probably slipped up somewhere.
Not checked Cam's stuff properly, but if Knightmare heads back, he should have 15 seconds spare.
Cam,
I disagree with that last statement.
We are given:
"He also calculates that by turning around and heading back, he will have just enough time to exit the bridge before the train reaches it"
Cam
Lol, that message was meant for you Chris not me. I must need some coffee if I'm starting to talk to myself.
Cam
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I now get 11 mph.
Houston we have a problem. K is 1/4 of the way across a bridge that he needs 3 minutes to cross, so he's 3/4 of a minute away from the end, so that gives him a margin of 1/4 min.
hi guys ... neither 17.14mph nor 11mph agrees with the published answer ... it could be wrong ... but you guys differ as well
Cam,LOL, RU trying to make one of those self-referential logic paradoxes?
Cam ... at least talking with yourself presents you with an intelligent discussion partner ... darn pain meds making me talk crazy ... heh heh.
22 miles/hour
22 miles/hour
I get 22 mph also.
Hi Zaux ...
yes ... 22 mph it is
oh wait ... that was intended for Cam ... this "talking to ones self" malady may be contagious
K starts 1/4 of the way, and would have got a further 2/3 of way (across bridge) in 2 minutes. SO K would have beeb 2/3 + 1/4 = 11/12 of way across. The train takes 1 min to cross 11/12 of bridge in 1 min and so 22/12 in 2 mins.
V = 8 * (22/12)/(2/3) = 22 mph
.. and I was drinking coffee, and Knightmare wants some of Zaux' meds.
heh heh ... he can have them, if he would also inherit the associated problems
... and I'm out of breath in the race with Cam ;)
you guys are great puzzlers and worthy competitors ...
I get 22mph if I Assume the following is false
"He also calculates that by turning around and heading back, he will have just enough time to exit the bridge before the train reaches it"
If Pequod can carry Knightmare back to the start (1/4) of the track.
And Pequod carries at 8 mph.
Then
8mph*1h/60minutes*1 minute= 8/60 miles
total bridge length = 3*8/60 miles=24/60=12/30
1/4 bridge length=3/30
if he is 15 seconds short of the edge if Pequod carries Knightmare forward then he is
15s*8mph*1h/60 minutes*1 minute/ 60 seconds=120/3600 miles=1/30 short of the end
so Pequod travels (total bridge length- 1/4 bridge length- 15s length)=12/30-3/30-1/30=8/30 miles
Time for pequod to travel 8/30 miles=8/30miles/8 mph=7/240h =1/30 h=2 min
Train is 1 minute to reach tracks so it only has 2-1=1 minutes
It travels (total bridge length- pequod's 15s length)=12/30-1/30=11/30 mile
11/30 mile/1 min*60 minutes/hour=22 mph
Answer:
Train travels at 22 mph
Cam
Cam is the better man though, by a healthy margin.
Only one of these two statements can be true.
"Upon approaching a long, familiar railroad bridge, he knows it will take 3 minutes for him to cross"
Answer: 22 mph
and
"He also calculates that by turning around and heading back, he will have just enough time to exit the bridge before the train reaches it" If he is 1/4 from the start of the bridge which he can reach in 1 minute.
Answer: 17.14 mph
Cam
Thanks for the compliments guys. You've got me blushing again.
Cam
Knightmare jogging...HA!
but really guys,you are thinking too much with all this math stuff.This bloke is so big that he can just stand still on the bridge(or maybe take a nap)without a worry in the world.the train will see him from far enough away that it will have plenty of time to stop(or risk derailing)
hi Pequod...that isn't funny.
Cam, you forgot that Knightmare has to change direction. That'll take up the 15 seconds.
... if his adrenalin glands still work.
yes they still work Chris...every time the pizza man comes to the door.
LOL.
22mph... or in real terms... a little too slow ;-)
10 2/3 mph
???? Anonymous, the question has been answered. 22 mph.
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