# Grumpy Old Men

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?

### 4 guesses to Grumpy Old Men

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• Golly Kim

Mr. Grumper adjusted his watch, not the station clock. So, the station clock was neither slow nor fast :)

• Dude

No, it’s not a trick question. There is a real answer to the riddle.

Keep trying.

• Golly Kim

The station clock was running fast by 3 minutes.

For calculation purpose, let us assume the distance as 60miles.
Any distance would lead to the same result.

Forward Journey:
The train covered the distance in 1hr 5 minutes (65m), so the
speed of the train was (60/65) miles/minute

Mr Grumper’s watch showed 3 minutes early. In essence, Mr G’s
watch was running 8 minutes slow. After he set forward his
watch by 3 minutes, the gap reduced to 5 minutes. That is,
his watch was running slow by 5 minutes.

Return Journey:
The train arrived at the boarding station on time according to
G’s watch. But actually, the train was running behind the schedule
by 5 minutes.

The train travelled 25% faster than the morning speed. That is,
the speed of the train on return journey was (60/65)x1.25 miles/min.
So, to cover 60 miles, the train took:
60/(60/65)x1.25 = 52 minutes instead of 60 minutes.
But train arrived at the boarding station 5 minutes late. So, if we
add this delay, the total time becomes 52+5 minutes = 57 minutes.

But the destination station’s clock showed the train arriving at
the right time (60 minutes). Which means, the station clock was
3 minutes fast.

• Dude

You are correct, Golly Kim!

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.

You are today’s winner.