Slow-running watch

Algebra Level 3

After going scuba-diving, Mei's watch (which was not water-resistant) started to run slower. By comparing to a clock on the wall, she realized that her watch was now running slow. In fact, for each minute that passed in real time, her watch got further behind by 10 seconds.

She tried to time the bus trip back to the resort. According to her watch, she boarded the bus at 10:00:00 AM, and reached the resort at 10:10:30 AM. How much time (in seconds) did the bus trip actually take?


The answer is 756.

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17 solutions

Rhoy Omega
Oct 27, 2013

In every minute passing in real life, the time passing in the watch is only (60-10) seconds or 50 seconds. Therefore, when n minutes had passed in real life, 50n seconds had passed in the watch. If ''a'' is the number of seconds that had passed in the watch,

a = 50n

The watch has recorded 630 seconds as the total time travel of the bus, so a = 630.

630 = 50n

630/50 = n

12.6 = n

Therefore, in real life 12.6 minutes had passed. Since 12.6 minutes equals 12.6(60) or 756 seconds, therefore, 756 seconds is the answer.

Moderator note:

Great explanation.

Most people who got this wrong set up the ratio and proportion poorly. The proper setup is:

50 Mei seconds : 60 real seconds 630 Mei seconds : ? ? real second \begin{array} { l l l } 50 \text{ Mei seconds } & : & 60 \text{ real seconds} \\ 630 \text{ Mei seconds} & : & ?? \text { real second} \\ \end{array}

Hence, by cross multiplying and dividing, the answer is 630 × 60 50 630 \times \frac{60}{50} .

For those who messed up their numbers, a common mistake was to give an answer of 630 × 50 60 630 \times \frac{50}{60} .

For those who misread the question, they set up the initial ratio as

60 Mei seconds : 70 real seconds 60 \text{ Mei seconds } : 70 \text{ real seconds}

This lead to answers of the form 630 × 70 60 , 630 × 60 70 , 630 × 10 60 630 \times \frac{70}{60}, 630 \times \frac{60}{70}, 630 \times \frac{10}{60} .

that was close ... 735 s !!

Fiza Khan - 7 years, 7 months ago

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See my note which explains why 735 = 630 × 70 60 735 = 630 \times \frac{70}{60} is incorrect, and how to identify the flaw in your argument.

Calvin Lin Staff - 7 years, 7 months ago

thanks for writing solution.

Sayan Mandal - 7 years, 7 months ago

Thanks

Pham Tung - 7 years, 7 months ago

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chao ban

kim ngan - 7 years, 7 months ago

thanks for the explanation

sonu sekar - 7 years, 7 months ago

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thanks for the explanation

sonu sekar - 7 years, 7 months ago

thank you

John Choi - 7 years, 7 months ago

Thanks

Priyanka Mekkat - 7 years, 7 months ago

thanx

Oshanto Zabir - 7 years, 7 months ago

thanks

Nesan TheHero - 7 years, 7 months ago

hmmmmmmmmmmmm

Mahin Roddur - 7 years, 7 months ago

756

Azhar Iqbal - 7 years, 7 months ago

thanhks

kim ngan - 7 years, 7 months ago

hmmmmmmmmmmm

Meena pinku - 7 years, 7 months ago

lol i was close :p

Momina Ahsan - 7 years, 7 months ago

konti na lang

Vincent Cagampang - 7 years, 7 months ago

Thanx 4 easy sol. I got cunfuse bec. Of this [ and many other signs

Summer Thapa - 7 years, 7 months ago

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hm

kim ngan - 7 years, 7 months ago

Great,,,

Kannia Kannia - 7 years, 7 months ago

Great thing..

Vaishnavi Swaminathan - 7 years, 7 months ago
Elin Daly
Oct 28, 2013

The bus trip took 10 minutes 30 seconds of time according to her watch. This is equal to 630 seconds (10*60+ 30). Her watch was running at 50 seconds for every 60 real time seconds (10 seconds less per minute (60-10 = 50)). This can be expressed as running at 50/60, simplified as 5/6, of real time. So, if the trip took 639 seconds at 5/6 speed, we can re-arrange, giving:

639/5 *6 = 756 seconds.

hmm

Mahin Roddur - 7 years, 7 months ago

756

kim ngan - 7 years, 7 months ago
Abubakarr Yillah
Jan 8, 2014

Since her watch goes 10 seconds further behind after every minute in real time, this means that at a one minute interval in real time her watch records 50 seconds.

i.e 1 m i n = 50 s {1min}={50s}

According to her watch she spent 10 minutes 30 seconds from where she boarded the bus to the resort

converting that time into seconds we get a total of 630 seconds

But we know that 1 m i n = 50 s {1 min}={50 s}

thus 630 seconds equals 1 × 630 50 \frac{1\times630}{50}

which gives 12.6 m i n s {12.6mins} in real time

converting this to seconds i.e. 12.6 × 60 {12.6\times60}

we get the required answer of 756 s \boxed{756s}

Finn Hulse
Jan 27, 2014

For every 60 seconds gone by, Mei's watch will go 50 seconds. After 630 of her seconds, we simply set up a proportion to solve. 50 / 60 = 630 / x. Solving for x, we get 756.

From 10 : 00 : 00 A M 10:00:00 AM to 10 : 10 : 30 A M 10:10:30 AM there are 630 630 seconds. Her minutes are of 50 50 seconds in her clock, so there's a total (in minutes) of 630 / 50 = 12.6 630/50 = 12.6 minutes. Now, each real minute has 60 60 seconds, so 12.6 60 = 756 12.6 * 60 = \boxed{756} .

Christopher Boo
Nov 6, 2013

If the REAL time is 60 seconds, then the SLOWED time is 50 seconds.

So we conclude that:

R E A L S L O W E D = 60 50 = 6 5 \frac{REAL}{SLOWED}=\frac{60}{50}=\frac{6}{5}

We knew that according to her watch she used 630 seconds, which is SLOWED,

R E A L S L O W E D = 6 5 \frac{REAL}{SLOWED}=\frac{6}{5}

R E A L 630 = 6 5 \frac{REAL}{630}=\frac{6}{5}

R E A L = 756 REAL=756

Rahul Kumar
Nov 25, 2013

As for 60 seconds in real time the watch completed only 50 seconds, we know that only 5 6th of the real time is completed by the watch per each minute. hence the watch reading falls back by 10 seconds with each passing minute. (Eg: for 60sec Real time -> 50 sec watch & then for 120 sec real time -> 100 sec watch time) thus for finding how much real time has passed for 630 seconds of watch time, (50/60)*x=630. And we get x as 756

Rai Kharal
Nov 13, 2013

Mei's watch 50 sec=6o sec actual = = 1 = 60|5o=1.2 sec actual.. eq.(1) now 10;10;30-10;10;00=630 sec 1.2*630= 756 ans

10*60+30=630 so 630x60/50=756

Mon Teruel
Nov 6, 2013

<p>10:10:30 - 10:00:00 = 00:10:30</p>

<p>10 min * 60 sec + 30 sec = 630 sec "watch duration"</p>

<p>630 sec / 50 sec = 12.6 min</p>

<p>12.6 min * 60 sec = 756 sec "actual duration"</p>

Gaurav Simha
Nov 6, 2013

To solve this problem, we must make use of the given fact that for every minute in actual time , the watch gets behind by ten seconds . Which means, for every minute, there will be a difference in time between the watch and real time; first equal to 10, then 20, then 30, and so on.

Thus, we can conclude the watch counts 50 seconds for each minute instead of 60 seconds. Therefore, the minute count of the watch is (5/6)th of a minute, instead of (6/6)th of a minute.

Let 'm' represent one minute in actual time. Total time elapsed in watch is 10min & 30sec = 10.5 min.

(5/6)m=10.5

m=63/5 (in minutes)

Thus, no. of seconds in 63/5 minutes = (63/5)*60= \boxed{756}

Scorpian .
Nov 6, 2013

Let the time taken in reality be "x" min ,then for each min the delay is by 10 sec therefore the time fed in the watch is 50 sec , its like a man's mind read 60 sec as 50 sec only always (each min is 50 sec for him ) . Now as she has travelled for "x" min , so 50 x = 630( 630 sec is the time in her watch ) So x= 63/5 min = (63/5) 60 sec ( why I have multiplied 50 and x ?...., becoz as the man can only remembers 50 sec for 60 sec , so in a long run i.e after x min he will remember only 50x sec ...).

Abhinav Mishra
Nov 6, 2013

For every every min(60 seconds) Mei's watch records 50 seconds passed, therefore actual time passed= (6/5) * time passed according to her watch. Here trip took 10*60+30 seconds= 630. therefore, 6/5 * 630 =756sceonds.

1 minute in her watch = 50 seconds every 6 seconds her watch got behind 1 second = 5 seconds that means the actual time = 6/5 the watch = 1.2 the watch the bus take 10 minutes 30 seconds = 630 seconds the actual time = 1.2 x 630 = 756 seconds

Akshay Krishnan
Oct 31, 2013

According to the problem, for every minute, the clock runs 10 secs slower. Therefore at end of every 50 secs in the slower clock, the actual clock would be ahead by 10 secs. So after every 5 secs in the slower clock, the actual clock is ahead by 1 sec. Which implies the actual time is equal to 630+(630/5)=756.

Leonardo Kumala
Oct 30, 2013

10.10.30 - 10.00.00 = 10.30 which is 630 seconds. Assume that the real time (in seconds) is x.

\­( 630 = x - \frac{x}{60} \times 10)

630 = x 10 x 60 630 = x - \frac{10x}{60}

630 + 10 x 60 = x 630 + \frac{10x}{60} = x

630 + x 6 = x 630 + \frac{x}{6} = x

5 y = 3780 5y = 3780

y = 756 y = \boxed{756}

Sorry, I type y is actually x

Leonardo Kumala - 7 years, 7 months ago
Rakhmat Muliawan
Oct 28, 2013

ratio time in watch : real time = (60 - 10) second : 60 second = 5 : 6 according time in watch has passed 630 seconds, so that real time is (630 : 5) x 6 = 756

hmm\

Mahin Roddur - 7 years, 7 months ago

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