# Homework Help: Watch problems gaining and losing time

1. Dec 3, 2015

### Natasha1

1. My watch (which is a 12 hour watch) gains 3 minutes every 2 hours.

a) I set my watch to the correct time at noon on 1st January. If I don't reset it, when will it next show the correct time?

I got 48 hours after, so that's at noon on the 3rd January. as if my watch gains 3 minutes every two hours then over 24 lots of 2 hours, it would have gained an extra 2 hours. So that is 24 lots of 2 hours = 24 x 2 = 48 hours added to the 'correct' starting time of noon. Hence, my answer of noon on the 3rd January.

2. Mrs Varma's watch (also a 12 hour watch) loses 5 minutes every 2 hours. She also sets her watch to the correct time at noon on 1st January.

b) When will our two watches next show the same time?

3. When will our watches next show the same, CORRECT time?

Again, I can't do this... Any explanation would be greatly appreciated. Thank you.

Nat.

2. Dec 3, 2015

### Samy_A

If you watch gains 3 minutes in 2 hours, it gains 3*12=36 minutes in a day. So it can't show the correct time after only two days.
Try to write the time on your watch as a function of the correct time.
Say $W(t)=$ some function of the correct time $t$ (expressed in minutes)
Then for your clock to again show the correct time, you should have $W(t)=t+720$ (because there are 720 minutes in 12 hours, and your clock has to gain 12 hours to again show the correct time). Solve that equation for $t$.

Use another similar function to represent the time on Mrs Varma's watch to solve 2) and 3).

Last edited: Dec 3, 2015
3. Dec 3, 2015

### Natasha1

Ok, I got January 4th at 8pm. Is this correct?

Cannot do 2b nor 3. Can anyone help me?

4. Dec 3, 2015

### Samy_A

It would help if you showed how you got that result.
I find something different. Note that your watch only gains 36 minutes a day, so it can't catch up in 3 days and 8 hours.

The time on your watch can be expressed as $W(t)=t+t*3/120$, where $t$ is the correct time in minutes, and $t=0$ represents noon on 1st January.
Your watch will again show the correct time when $W(t)=t+720$.

So we look for the solution of $$t+t*3/120=t+720$$
Express the time on Mrs Varma's watch by a function $V(t)$, similar to the function $W(t)$ expressing the time on your watch.

Last edited: Dec 3, 2015
5. Dec 3, 2015

### PeroK

Why not try this to get you started and let you see what's going on. Keep two lists: one with the correct time and one with the time your watch shows. For 1a:

Correct Time / My Watch

Jan 1st noon / noon
Jan 1st 2.00 (pm) / 2.03
Jan 1st 4.00 (pm) / 4.06
Jan 1st 6.00 (pm) / 6.09

6. Dec 3, 2015

### Natasha1

Ok,

a) I set my watch to the correct time at noon on 1st January. If I don't reset it, when will it next show the correct time?

I got 8pm (or 20.00) on 4th January. Can someone tell me if I am right?

2. Mrs Varma's watch (also a 12 hour watch) loses 5 minutes every 2 hours. She also sets her watch to the correct time at noon on 1st January.

b) When will our two watches next show the same time?

I got 25th January at noon (lunchtime). Am I right?

3. When will our watches next show the same, CORRECT time?

I got 19th February at noon (lunchtime). Am I right?

7. Dec 3, 2015

### Samy_A

No, not correct.
No, not correct.

No, not correct.

If you find my approach with the function too difficult, why don't you try what @PeroK suggested for 1a)?

8. Dec 3, 2015

### PeroK

Given your answer to 1a, I don't think you've understood the problem. Imagine your watch really was 3 mins fast every 2 hours, that's only 36 minutes a day. It will, therefore, take weeks until it shows the correct time again.

I wouldn't look at questions 2 and 3 until you've understood problem 1. Go back to my suggestion in post #5 to give yourself an idea of what's happening.

9. Dec 3, 2015

### Natasha1

if it gains 36mins in every 24 hours then for my watch to catch up time it will have to be 1440/36 = 40 so forty days from 1st of January which would be 10th February at noon.

Is this correct?

10. Dec 3, 2015

### haruspex

Much better, but remember it is a 12 hour watch. How fast will it be when it first shows the correct time?

11. Dec 3, 2015

### PeroK

That's much closer.

How many hours (on a 12-hour watch) does it need to gain to catch up? The question assumes you know that on a 12-hour watch, no distinction is made between 12 noon and 12 midnight. Perhaps you're one of those people who never wears a watch?

12. Dec 3, 2015

### Natasha1

Oh!! I did not know about this! It's so confusing... No I do not have a watch, and only really get 24hrs clocks.

is it 20 days later? Is it 720/36 = 20 so on 21st of January at noon. If so, why?

13. Dec 3, 2015

### PeroK

I think you've got the idea. Here's the sort of thing they're talking about:

14. Dec 3, 2015

### Samy_A

Yes.

Your watch has to gain 12 hours, that's 12*60=720 minutes. As it gains 36 minutes a day, it shows the correct time again after 720/36=20 days.

15. Dec 3, 2015

### Natasha1

I see! Thanks.... So for:

2)
Thanks :)... Much clearer!

16. Dec 3, 2015

### Natasha1

Not sure how to go about 2 and 3

17. Dec 3, 2015

### haruspex

How far apart are the two watches after one hour? How far apart do they need to be to be showing the same time?

18. Dec 3, 2015

### Natasha1

they are 8 mins apart... then 16 then 24.. Ahhh so when does 8 fit into multiples of 60, right?

19. Dec 3, 2015

### Natasha1

8
16
24
32
40
48
56
64
72
80
88
96
104
112
120

So that's 30 hours after.... So that would be 2nd January at 6pm? Is this right?

20. Dec 3, 2015

### haruspex

I said "after one hour".
And you did not answer my second question: how far apart will they be when they first show the same time again?