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## Question

Mr. Grumper grumbles about bad time-keeping trains like everybody else. On one particular morning he was justified, though. The train left on time for the one hour journey and it arrived 5 minutes late. However, Mr. Grumper's watch showed it to be 3 minutes early, so he adjusted his watch by putting it forward 3 minutes. His watch kept time during the day, and on the return journey in the evening the train started on time, according to his watch, and arrived on time, according to the station clock. If the train traveled 25 percent faster on the return journey than it did on the morning journey, was the station clock fast or slow, and by how much?

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Which station clock? There is a 5 min difference between the two.

If the train leaves at 8 and arrives at 9:05 then the second station is 5 minutes fast given a one hour ride. At this time the mans watch is set for 9 to match the first stations time. To leave the station in the afternoon at 5 (man/first station) the second station would have to be 5:05. Train takes 45 mins to get back to the first station which would be 5:45 (man/first station) or 5:50 at the second station.

Edited by curr3nt
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The station clock is 6 minutes and 15 seconds fast.

When the train arrives in the morning 5 minutes late, My grumper adjusts his watch to the hour, which is thus 5 minutes slow. This means that on the way back, when the train starts on time according to his watch, the train is still 5 minutes behind schedule. So if it were 5pm on his watch, then the train started at 5:05 pm.

The train then goes 25% faster than when it started. since it took an hour and 5 minutes the first time, 25% faster takes 48 minutes and 45 seconds. This means that the train arrives at 5:53 and 45 seconds in reality. Since the station clock shows the train to be arriving on time, it must show 6:00 which is 6 minutes and 15 seconds fast.

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The station clock is 6 minutes and 15 seconds fast.

When the train arrives in the morning 5 minutes late, My grumper adjusts his watch to the hour, which is thus 5 minutes slow. This means that on the way back, when the train starts on time according to his watch, the train is still 5 minutes behind schedule. So if it were 5pm on his watch, then the train started at 5:05 pm.

The train then goes 25% faster than when it started. since it took an hour and 5 minutes the first time, 25% faster takes 48 minutes and 45 seconds. This means that the train arrives at 5:53 and 45 seconds in reality. Since the station clock shows the train to be arriving on time, it must show 6:00 which is 6 minutes and 15 seconds fast.

By your reasoning the clocks are in synch at the two stations. So you suggest that the train can leave at 5:05 from one station, travel for almost 49 mins and arrive at 6:00 at the other. This is why I assumed the stations are not in synch and when he said an hour long train ride that is what he meant, not a 65 minute ride.

edit for bad grammar...not to say there isn't more to be found

Edited by curr3nt
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By your reasoning the clocks are in synch at the two stations. So you suggest that the train can leave at 5:05 from one station, travel for almost 49 mins and arrive at 6:00 at the other. This is why I assumed the stations are not in synch and when he said an hour long train ride that is what he meant, not a 65 minute ride.

edit for bad grammar...not to say there isn't more to be found

The question only mentions one station clock. It doesnt say anything about there being two different station clocks. All it says is that the train leaves on time (in reality) in the morning, arrives 5 minutes late, the mans watch was adjusted at this point to assume the train arrived on time (in other words to the hour). Then in the afternoon, the train starts on time according to his newly set watch, and then arrives on time according to the stations clock, which i admit i assumed was the station that the train arrived at. Either way there are only two clocks in question.

I am not suggesting that the train can leave from one station at 5:05, travel for almost 49 minutes and arrive at 6:00 pm. What i am saying, however, is that if the train leaves at 5:05 from one station (which is late because it was supposed to leave on the hour), travels for almost 49 minutes, and then arrives at the other station, then the question dictates that this station's clock is indicating that the train is arriving on time. In other words, when the train arrives at the station, the clock is showing that it arrived when it was supposed to, which is on the hour at 6:00pm. This suggests that because the actual time is earlier that 6:00, the station clock must be running fast. specifically 6 minutes and 15 seconds per my earlier post.

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I think that the train took 65 minutes on the first trip, but the question states that it left on time (not according to anyone's watch). The fact that he adjusted his watch is moot because it apprently kept time all day long, So when the train left on time (let's say 5pm) and got to the station 25% quicker, it arrived at 5:48:45. The station clock said 6pm and was 11.25minutes fast.

This seems like a subjective problem, though,depending how you read it.

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I think that the train took 65 minutes on the first trip, but the question states that it left on time (not according to anyone's watch). The fact that he adjusted his watch is moot because it apprently kept time all day long, So when the train left on time (let's say 5pm) and got to the station 25% quicker, it arrived at 5:48:45. The station clock said 6pm and was 11.25minutes fast.

This seems like a subjective problem, though,depending how you read it.

I think we read this the same way except that i dont think left on time though on the return trip. It left on time according to the man's watch, which was 5 minutes slow - because he set it that way after the morning train which he assumed was on time even though it was in reality 5 minutes late. thats why i got 6.25 minutes fast instead of 11.25 minutes fast.

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the station clock is 13 minutes fast.

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I think I got it:

The train took 65 mins to get there and 48:25 mins to get back. Mr.Grumper set his watch to the station time, which showed that the train was on time. But it was actually 5 minutes late so the station clock was 5 minutes slow. Because I think i might have messed up on my fasts and slows so my second answer (unlikley) is 2 minutes slow. Before Mr.Grumper "fixed" his watch, his watch was 8 minutes slow.

Edited by Jetdron
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For some reason, people seem to think that "traveled 25 percent faster" means "arrived in 75% of the time." Traveled means rate, so the rate is 1.25x the rate, and time is then 1/1.25. So the first journey, taking 1 hour and 5 minutes, will now take 65/1.25 minutes, or 52 minutes.

Say the train leaves at *true* 9 AM, arrives at true 10:05 AM, and Mr. Grumper sets his watch for 10:00 AM (He saw that it arrived at 9:57, and adjusted so that it arrived at "10:00"). The day has passed, Mr. Grumper finishes doing whatever it is that grumpy old men do, and returns home. The train leaves at 4:00 PM (according to his watch), where in reality it left at 4:05 PM (the train was late again, but he didn't know!). He arrives 52 minutes later, at true 4:57 PM, however the station clock says 5:00 PM. The station clock is 3 minutes fast.

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For some reason, people seem to think that "traveled 25 percent faster" means "arrived in 75% of the time." Traveled means rate, so the rate is 1.25x the rate, and time is then 1/1.25. So the first journey, taking 1 hour and 5 minutes, will now take 65/1.25 minutes, or 52 minutes.

Say the train leaves at *true* 9 AM, arrives at true 10:05 AM, and Mr. Grumper sets his watch for 10:00 AM (He saw that it arrived at 9:57, and adjusted so that it arrived at "10:00"). The day has passed, Mr. Grumper finishes doing whatever it is that grumpy old men do, and returns home. The train leaves at 4:00 PM (according to his watch), where in reality it left at 4:05 PM (the train was late again, but he didn't know!). He arrives 52 minutes later, at true 4:57 PM, however the station clock says 5:00 PM. The station clock is 3 minutes fast.

SOLVED1 by snelltaylor!

The morning journey took 65 minutes, and the evening journey therefore took 52 minutes, and the train arrived 57 minutes after it should have left, that is, 3 minutes early.

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For some reason, people seem to think that "traveled 25 percent faster" means "arrived in 75% of the time." Traveled means rate, so the rate is 1.25x the rate, and time is then 1/1.25. So the first journey, taking 1 hour and 5 minutes, will now take 65/1.25 minutes, or 52 minutes.

Say the train leaves at *true* 9 AM, arrives at true 10:05 AM, and Mr. Grumper sets his watch for 10:00 AM (He saw that it arrived at 9:57, and adjusted so that it arrived at "10:00"). The day has passed, Mr. Grumper finishes doing whatever it is that grumpy old men do, and returns home. The train leaves at 4:00 PM (according to his watch), where in reality it left at 4:05 PM (the train was late again, but he didn't know!). He arrives 52 minutes later, at true 4:57 PM, however the station clock says 5:00 PM. The station clock is 3 minutes fast.

nice job

Edited by Jetdron

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