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February 24th, 2019, 12:02 PM   #1
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Question How do I find the time of a scheduled event if it is given between a range?

I'm going in circles with this riddle. It doesn't appear too complicated but I got tangled with the *right* interpretation of the *time* mentioned.

The problem is as follows:
At a TV station a program director decides to set a new schedule for the morning news show. He decides that the show is to start after 5 am but before 8 am. If we know that the elapsed time between 5 am until 25 minutes before the show begins is equal to two thirds of the time which will be to 8 am but in 25 minutes. What time does the show starts?.
The existing alternatives in my book are as follows:

$\begin{array}{ll}
1.& \textrm{7:17 AM}\\
2.& \textrm{5:37 AM}\\
3.& \textrm{6:27 AM}\\
4.& \textrm{5:47 AM}\\
5.& \textrm{6:17 AM}\\
\end{array}$

What I tried to do was the following. It's a bit tricky but I thought that the unknown time to be $x$ and built the equation from there given these interpretations:

Time elapsed between $25$ minutes before the start of the show and $\textrm{5 AM}$:

$\left(x-\frac{1}{4}\right)-5$

Time which is two thirds which will be to $8$ am but in $25$ minutes:

$8-\left(\frac{2}{3}+\frac{25}{60}\right)$

For this part and as well for the previous I'm working using hours and not minutes so by the end I can get a straight answer.

Since it mentions that both are equal then it is just plugging in together:

$\left(x-\frac{1}{4}\right)-5=8-\left(\frac{2}{3}+\frac{25}{60}\right)$

$x=13+\frac{1}{4}-\frac{2}{3}-\frac{5}{12}$

$x=13+\frac{3-8-5}{12}$

$x=13-\frac{16}{12}=13-\frac{4}{3}=12-1-\frac{1}{3}=11-\frac{1}{3}$

Then I interpreted the last line as:

$11 - \frac{1}{3}\times 60 = 11 - 20m$

Hence the time would be:

$\textrm{10 AM 40 mins}$

But this is clearly outside the boundary which is established on the problem.

Then I thought that the right interpretation would be:

Time which is two thirds which will be to $8$ am but in $25$ minutes:

$\frac{2}{3}\left(8-\frac{25}{60}\right)$

Hence:

$\left(x-\frac{1}{4}\right)-5=\frac{2}{3}\left(8-\frac{5}{12}\right)$

Multiplying by $36$ all:

$36x-9-180=192-10$

$36x=189+182$

$36x=371$

Simplifying the last result yields: $\textrm{1h 18m 20s}$. This result is not even close. Can somebody help me which is the part where I got lost or what I did not interpreted correctly? I reviewed the equations over and over and still I cannot figure out what I did wrong. Can somebody help me with this?

Last edited by skipjack; February 24th, 2019 at 04:29 PM.
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February 24th, 2019, 01:32 PM   #2
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Check again the part $\displaystyle x=13+1/4 -2/3 -5/12$ .
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February 24th, 2019, 05:44 PM   #3
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$x = 5 + \frac{\large5}{\large12} + \frac{\large2}{\large3}\left(8 - x - \frac{\large5}{\large12}\right) \\$
$\therefore x = 3 + \frac{\large1}{\large4} + \frac{\large16}{\large5} - \frac{\large1}{\large6} = 6 \frac{\large17}{\large60}$ (6:17 AM)
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February 24th, 2019, 08:08 PM   #4
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Quote:
Originally Posted by skipjack View Post
$x = 5 + \frac{\large5}{\large12} + \frac{\large2}{\large3}\left(8 - x - \frac{\large5}{\large12}\right) \\$
$\therefore x = 3 + \frac{\large1}{\large4} + \frac{\large16}{\large5} - \frac{\large1}{\large6} = 6 \frac{\large17}{\large60}$ (6:17 AM)
Yay!. It looks that the $x$ appears in the right side of the equation. Can you tell me the reason. Because I have been trying to look for a justification in all my attempts but I couldn't find any.
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February 24th, 2019, 08:17 PM   #5
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The wording "but in 25 minutes" doesn't really make sense, so I assumed "from 25 minutes after the show begins" was intended. Perhaps the question wasn't originally in English and has suffered in translation.
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February 25th, 2019, 02:13 PM   #6
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Quote:
Originally Posted by skipjack View Post
The wording "but in 25 minutes" doesn't really make sense, so I assumed "from 25 minutes after the show begins" was intended. Perhaps the question wasn't originally in English and has suffered in translation.
I was also suffering from the interpretation of that specific words. However by looking at your equation it appears that you interpreted as 25 minutes before the show begins because it is shown as:

$\left(8-x-\frac{25}{60}\right)$

While I do understand the part where $(x-\frac{5}{12})-5$ as it is clear to be the time between 5 AM and 25 minutes before the show to start. Why exactly are you subtracting $x$ from 8 AM?. This is the part where I'm stuck at. Does it exist a reason?

In the problem I cannot really understand that or how it was meant. Can you please explain me how did you understood that part and your reasoning to subtract $x$ from 8 AM please?.
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February 25th, 2019, 04:20 PM   #7
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Think of it as $\left(8 - \left(x + \frac{\large25}{\large60}\right)\right)$, which is the time "to 8 AM from 25 minutes after the show begins".
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February 26th, 2019, 05:53 AM   #8
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Think of it as $\left(8 - \left(x + \frac{\large25}{\large60}\right)\right)$, which is the time "to 8 AM from 25 minutes after the show begins".
Okay I got that part but why $x$ is also on the right side of the equation?. I read the passage countless times and I still can't figure out a reason.

When it said, two thirds of the time which will be to 8 AM etc.. how do I conclude that this "time" they are referring has to be also $x$ in other words the "same" time which is when the show is to start?. I revisited the problem to look for a reason but in the end I couldn't find any, in fact it made to think that the logical option would be not including that $x$ and be just $\frac{2}{3}\left(8+\frac{25}{60}\right)$, but it turns out not to be the case.

This is the part where I'm confused, can you enlighten me a bit on this please?

I'm sorry maybe I'm dumb as a rock with this problem.

Well, I've read it again and now it is clear. Or at least I think so. The reason why $x$ appears in the right side of the equation by going on this interpretation is because $x$ is the time when the show begins and $x+\frac{25}{60}$ is the time 25 minutes after when the show begins; this subtracted from 8 and two thirds of that will get the result.

Am I understanding it correctly skipjack? Again, I'm sorry, but my mind is like an 8-bit computer and takes time to get that ah-ha moment.

Last edited by skipjack; February 26th, 2019 at 08:46 AM.
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February 26th, 2019, 08:42 AM   #9
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The problem's second sentence ends with "the time which will be to 8 am but in 25 minutes", but doesn't have a "from" clause to specify when the intended elapsed time begins. As the wording "but in 25 minutes" seems to be intended to contrast with the earlier wording "and 25 minutes before the show begins", I effectively assumed that the intended meaning of "in 25 minutes" was "from 25 minutes after the show begins".
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