Watch problems gaining and losing time

[Natasha1]

what do I do from here?

 

[Samy_A]

it loses 5x12 = 60 mins in a 12 hour day

No, the difference grows by 8 minutes every 2 hours, so that makes 8*12=96 minutes in a day (a real 24 hours day).
But a difference of 96 minutes doesn't make the watches show the same time.
As the difference continues to grow, how big has it to become for the watches to again show the same time?

EDIT: my 24-hour watch says 23.39pm, good night.

 

[Natasha1]

This is too hard for me... I'm lost.

720 (not sure why but there you go) / 96 = 7.5 days so the answer would be 9th January at midnight

 

[SammyS]

How far apart time-wise do the two watches have to in order that they show the same time as each other?

Did haruspex ask that a few times already ?

 

[Natasha1]

Yes and this is what I answered...

After (in hours) Mrs Varma's watch My watch
1 2.5 1.5
2 5 3
3 7.5 4.5
4 10 6
5 12.5 7.5
6 15 9
7 17.5 10.5
8 20 12
9 22.5 13.5
10 25 15
11 27.5 16.5
12 30 18
13 32.5 19.5
14 35 21
15 37.5 22.5So after 15hrs or 3am on 2nd January will our two watches show the same time.

 

[Natasha1]

Can anyone just explain to me by doing it? As I have tried time and time again (proof in my threads)... But simply don't get it?

 

[SammyS]

Can anyone just explain to me by doing it? As I have tried time and time again (proof in my threads)... But simply don't get it?

He did NOT ask how much time must elapse so that the watches read the same time again. He asked how far apart they must be relative to each other when they display the same thing.

 

[Samy_A]

Yes and this is what I answered...

After (in hours) Mrs Varma's watch My watch
1 2.5 1.5
2 5 3
3 7.5 4.5
4 10 6
5 12.5 7.5
6 15 9
7 17.5 10.5
8 20 12
9 22.5 13.5
10 25 15
11 27.5 16.5
12 30 18
13 32.5 19.5
14 35 21
15 37.5 22.5So after 15hrs or 3am on 2nd January will our two watches show the same time.

After 15 hours the difference is 60 minutes, or 1 hour. But these are 12 hour watches, not 1 hour watches. That's why they don't show the same time after 15 hours.

This is too hard for me... I'm lost.

720 (not sure why but there you go) / 96 = 7.5 days so the answer would be 9th January at midnight

Yes, the 7.5 days is correct.

Why?

Well, you know that the difference between the two watches grows by 96 minutes a day.
What does it mean that the difference between the two watches is 96 minutes (1 hour and 36 minutes)? It means that if your watch is (hypothetically) at 12.00 noon, Mr Varma's watch will be 96 minutes behind, that is 10.24 am.
After two days the difference between the two watches is 192 minutes (3 hours and 12 minutes). It means that if your watch is (hypothetically) at 12.00 noon, Mr Varma's watch will be 192 minutes behind, that is 8.48 am.
And so on.

When will the two watches again show the same time? Well, when the difference between them will have gone full circle, meaning 12 hours.
12 hours = 720 minutes. When the difference is 12 hours, the watches again show the same time, precisely because these are 12 hour watches.
That's why you divided 720 by 96 to get the correct result.

 

[Samy_A]

How on Earth do I work out 3?

You already established in the first question that your watch will again show the correct time after 20 days.
That means it will also show the correct time after 20+20=40 days. And also after 40+20=60 days. And so on.

Now, before solving 3, try to establish after how many days Mrs Varma's watch will again show the correct time. This is similar to the first exercise.

 

[Natasha1]

Does that mean that Mrs Varma's watch which loses 5mins every 2 hours then loses 60 mins in 12 hours(or 720 mins)

So Mrs Varma's watch will show the correct time in 720/60 = 12 days and because my watch in 720/36 = 20 days they will both show the correct time in

60 days as this is the lowest common multiple.

Is this correct?

 

[Samy_A]

Does that mean that Mrs Varma's watch which loses 5mins every 2 hours then loses 60 mins in 12 hours(or 720 mins)

So Mrs Varma's watch will show the correct time in 720/60 = 12 days and because my watch in 720/36 = 20 days they will both show the correct time in

60 days as this is the lowest common multiple.

Is this correct?

Yes.

 

[Natasha1]

Thank you :)

 

[dgsspkumar]

Answers
1. Gained time = 12 hours = 720 min
After t hours
t×3/120 = 12
t=480 hours=20 days
Jan 21 St at noon
2. To show same time, time gained in one watch should be equal to 12 hours minus time lost in other watch. It can even be vice versa.
Time gained = 12 - time lost
t * 3/120 = 12 - t* 5/120
t = 240 hours = 10 days
Jan 11 at noon
3 . the clocks show same time every 10 days
The clock shows right time after 20 days ( from problem 1)
Hence both clocks show correct same time after 20 days
Jan 21 at noon

 

[Samy_A]

Answers
1. Gained time = 12 hours = 720 min
After t hours
t×3/120 = 12
t=480 hours=20 days
Jan 21 St at noon

Correct.

2. To show same time, time gained in one watch should be equal to 12 hours minus time lost in other watch. It can even be vice versa.
Time gained = 12 - time lost
t * 3/120 = 12 - t* 5/120
t = 240 hours = 10 days
Jan 11 at noon

t * 3/120 = 12 - t* 5/120 is correct, but then you made a computation error.

3 . the clocks show same time every 10 days
The clock shows right time after 20 days ( from problem 1)
Hence both clocks show correct same time after 20 days
Jan 21 at noon

Not correct, as based on wrong result for 2).

 

[dgsspkumar]

1. Gained time = 12 hours = 720 min
After t hours
t×3/120 = 12 t=480 hours=20 days
Jan 21 St at noon
2. To show same time, time gained in one watch should be equal to 12 hours minus time lost in other watch. It can even be vice versa.
Time gained = 12 - time lost
t * 3/120 = 12 - t* 5/120
t = 180 hours = 7days 12 hours
Jan 8 mid night
3. The clocks show same time every 7days 12 hours.
The 1 st clock shows right time after 20 days ( from problem 1)
The answer is a common multiple of 7.5 and 20.
60 days
Hence Clocks show correct same time after sixty days
jan 1 to jan 31 - 30 days
feb 1 to feb 28 - 28 days
jan 1 and jan 2
hence answer is Jan 2 noon

Reference https://www.physicsforums.com/threads/watch-problems-gaining-and-losing-time.846247/page-3

 

[dgsspkumar]

Correct.
t * 3/120 = 12 - t* 5/120 is correct, but then you made a computation error.
Not correct, as based on wrong result for 2).

1. Gained time = 12 hours = 720 min
After t hours
t×3/120 = 12 t=480 hours=20 days
Jan 21 St at noon
2. To show same time, time gained in one watch should be equal to 12 hours minus time lost in other watch. It can even be vice versa.
Time gained = 12 - time lost
t * 3/120 = 12 - t* 5/120
t = 180 hours = 7days 12 hours
Jan 8 mid night
3. The clocks show same time every 7days 12 hours.
The 1 st clock shows right time after 20 days ( from problem 1)
The answer is a common multiple of 7.5 and 20.
60 days
Hence Clocks show correct same time after sixty days
jan 1 to jan 31 - 30 days
feb 1 to feb 28 - 28 days
jan 1 and jan 2
hence answer is Jan 2 noon
Is this correct now ?

 

[Samy_A]

1. Gained time = 12 hours = 720 min
After t hours
t×3/120 = 12 t=480 hours=20 days
Jan 21 St at noon
2. To show same time, time gained in one watch should be equal to 12 hours minus time lost in other watch. It can even be vice versa.
Time gained = 12 - time lost
t * 3/120 = 12 - t* 5/120
t = 180 hours = 7days 12 hours
Jan 8 mid night
3. The clocks show same time every 7days 12 hours.
The 1 st clock shows right time after 20 days ( from problem 1)
The answer is a common multiple of 7.5 and 20.
60 days
Hence Clocks show correct same time after sixty days
jan 1 to jan 31 - 30 days
feb 1 to feb 28 - 28 days
jan 1 and jan 2
hence answer is Jan 2 noon
Is this correct now ?

Yes.

(I mean the sixty days for 3. You probably made a typo at the end, where you meant March and not January.)

 

[dgsspkumar]

Yes.

(I mean the sixty days for 3. You probably made a typo at the end, where you meant March and not January.)

Ya it was march 2 noon.