Logic-Time

Kodwo · **Posted:** Wed, 28 Sep 2011 15:06:54 UTC

A clock loses 10 minutes each hour.
If the clock is set correctly at noon,

what time is it when it reads 3 PM?

I want to be able to make some meaning out of this question.How do I approach it?

Soroban · **Posted:** Wed, 28 Sep 2011 15:49:23 UTC

Hello, Kodwo!

An interesting problem . . .
It took a few tries to get an approach.

Quote:

A clock loses 10 minutes each hour.
If the clock is set correctly at noon, what time is it when it reads 3 PM?

Suppose we have two clocks: one which is accurate, the other loses 10 minute per hour.

Let

= number of minutes the accurate clock moves.
Let

= number of minutes the slower clock moves.

We know that: . $S \,=\,\frac{5}{6}A$

When the slower clock shows 3 PM, it has moved 180 minutes: . $S \,=\,180$

. . Hence: . $180 \,=\,\frac{5}{6}A \quad\Rightarrow\quad A \,=\,216$

The accurate clock has moved 216 minutes.
. . The time will be 3:36 PM.

Kodwo · **Posted:** Sun, 2 Oct 2011 18:03:30 UTC

Thanks Soraban,

I have just been looking at the answer you supplied.

How did you get 5/6?

If the NOT accurate clock loses 10 minutes every hour between 12noon and 3pm( 3hours/180 minutes) it would have lost 30 minutes RIGHT?

I am lost and confused

Shadow · **Posted:** Sun, 2 Oct 2011 18:45:13 UTC

Kodwo wrote:

Thanks Soraban,

I have just been looking at the answer you supplied.

How did you get 5/6?

If the NOT accurate clock loses 10 minutes every hour between 12noon and 3pm( 3hours/180 minutes) it would have lost 30 minutes RIGHT?

I am lost and confused

Remember it doesn't lose things all at once and it's asking what the REAL time will be when the BAD clock reads 3:00 pm.

aswoods · **Posted:** Sun, 2 Oct 2011 19:18:12 UTC

After 60 minutes have passed, the clock thinks that only 50 minutes have passed.

So clock time is 50/60 = 5/6 of real time.
Conversely, real time is 6/5 of clock time.

Thus at 3pm, the clock reads 2.30pm.
And at 3.36pm, the clock reads 3pm.

Kodwo · **Posted:** Sun, 2 Oct 2011 23:53:18 UTC

Thanks everyone I got it now:

Let me try my hands on a similar question here:

A clock loses 15 minutes each hour. If the clock is set correctly at 1 pm, what time is it when it reads 5 pm?

Real Time = 3/4*Clock Time

Real Time = 3/4*240 minutes = 180 minutes

5:00 pm + 180 minutes = 8:00 pm

Hope I am right?

Thanks

Kodwo · **Posted:** Mon, 3 Oct 2011 00:30:43 UTC

I corrected myself before anyone saw it

Real Time = 4/3*Clock Time

Real Time = 4/3*240 minutes = 320 minutes(5 hours 20 min)

1:00 pm + 320 minutes = 6:20 pm

Hope I am right?

aswoods · **Posted:** Mon, 3 Oct 2011 01:34:48 UTC

Kodwo wrote:

Real Time = 4/3*Clock Time

Real Time = 4/3*240 minutes = 320 minutes(5 hours 20 min)

1:00 pm + 320 minutes = 6:20 pm

That's correct.

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