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Grade 7/8 POTW: Info: - Gains 10 seconds everyday - How many times will it show the correct time from age 12 to 90
I remember trying to do this last year and getting some large number that didn't make much sense, so I'm hoping that I learned from my mistakes and don't multiply some large number by some other large number. Using common sense, we know that the watch will be correct after 12 hours (because am and pm do not matter here) which is 43200 seconds long. Since the watch gains 10 seconds per day, we can divide 43200 by 10 to get 4320 (approx. 11.8 years) until there is a correct time again. There are 78 years from 12 to 90, so we can take 78 and plug it into this wonderful equation seen below this nice smiley face. c: years/(years until correct time) 78/11.8= approx. 6.6 And since a watch can't be correct 6.6 times, the answer is 6 times. Yay. :))))))))
RWA-ish: - Jeff probably should get a new watch soon because then he'll be late for all his meetings and this watch will render useless.
Wait isn't the watch supposed to be good, not stopped? If it was good I don't think it would be correct every 12 hours(probably a much longer period of time).
I assumed this question meant that the watch would gain 10 seconds at the end of the day. So, it would be normal(ish) for the whole day, then when it reaches midnight of the next day, it would gain 10 seconds.
GRADE 7/8 POTW the solution to this POTW is quite simple. In my opinion, you have to find out how many seconds pass on the watch in 78 years and then divide by the number of seconds in 12 hours. 10 seconds= 1 day . 365 days x 10=3650= 1 year 3650 x 78= 284700= Number of seconds in 78 years
Number of Seconds in 12 hours= 60x60x12=43200 seconds in 12 hours
284700/43200= 6.6 Approx. 6.6 is not an integer so 6 is the answer.
The clock will show the correct time 6 times from the age of 12 to 90.
Maruti Seconds in a day 60 x 60 x 24 = 86400 Since it gains 10 seconds divide that by 10 and it will take 8640 days to show the correct time. There are 28468 days because the 12 and 90 birthdays are excluded. Divide 28468 by 8640 equals 3.3 approximately but there is P.M. and A.M. so multiply it by 2 so you get 6.6. Since you have to round down because there can't be extra days it will show the correct time 6 times from that time frame.
Aliyah Meltz 90-12=78 years Since the watch gains ten seconds per day and there is 365 days per year then 365x10=3650. To find the amount of seconds in 78 years then you multiply 3650x78=284,700
Now since the watch will obviously be correct every 12 hours than since there are 43,200 seconds in 12 hours then 284,700/43,200=6.6
Because we must round 6.6 then the watch will show the correct time 6 times from Jeff's age 12-90.
90-12=78 10 seconds every day 10*365.25=3652.5 seconds in a year 3652.5*78=284,895 seconds in 78 years now divide this by the number of seconds in 12 hours (half a day) 12*60*60=43200 284,895/43,200 =it equals about 6 so based on that we can assume that it is only six times because it only hits the exact time 6 times it can't be 6 and 1 half or anything else.
There are 365 days in a year, and we must multiply 10 and 365 to find how many seconds in a year. (3650) Then, we need to multiply by the remaining number of years until he reaches 90. Jeff's age= 12 Age required= 90 90-12=78
3650*78=255500+29200=284700 Based off what I know about clocks (I'm not an expert), every half day should count because the clock ticks 2 rotations in a day. The seconds in half a day are 12 hours*60*60=43200
We then divide 284700 by 43200 because that is the total time divided by the time taken for one correct rotation. 284700/43200 roughly equals 6.5, however, we still round down because half a tick does not count as a tick.
Therefore, the watch shows the correct time 6 times. *le gasp*
First we need to figure out the amount of seconds in one year, if the watch gains 10 seconds every day: 365 x 10 = 3650. He will turn 90 in 78 years, as 90 - 12 = 78 3650 x 78 = 284700.
Each day has 12 hours. There are 3600 seconds in every hour: 3600 x 12 = 43, 200
Now, we divide 284700 by 43, 200 giving us 6.590, rounded to 6.6, rounded to 6.
Seconds in a day 60 x 60 x 24 = 86400 The watch gains 10 seconds each day, so you would divide that by 10 (8640) and it will take 8640 days to show the correct time. There are 28470 days between the 12th and 90th birthdays Divide 28468 by 8640 equals 3.3 approximately. Since there is P.M. and A.M. you would have to multiply it by 2 so you get 6.6. Since you have to round down because there can't be extra days added, it will show the correct time 6 times from when he is 12.
First find the number of second in a day 60*60*24=86400 Then you need to find how many days it will take for the watch to show the correct time which would be total seconds divided by 10. 8640 days Then find the days in 78 years (90-12) 28468 Then divide and you get 3.3 for each 12 hours. multiply by 2 for 1 day 6.6 then go down because you are counting the number of days and you can't have half a day. 6 times
The watch would gain 1 hour in 60*6 or 360 days, therefore it will gain 12 hours in 12*360= 4,320 days which is equal to 4,320/365 or around 11.8 years.
Between the age of 12 and 90 there are 78 years, so 78/11.8=6.6, so it would have shown correct time 6 times by the time he is 90.
Grade 7/8 POTW:
ReplyDeleteInfo:
- Gains 10 seconds everyday
- How many times will it show the correct time from age 12 to 90
I remember trying to do this last year and getting some large number that didn't make much sense, so I'm hoping that I learned from my mistakes and don't multiply some large number by some other large number. Using common sense, we know that the watch will be correct after 12 hours (because am and pm do not matter here) which is 43200 seconds long. Since the watch gains 10 seconds per day, we can divide 43200 by 10 to get 4320 (approx. 11.8 years) until there is a correct time again. There are 78 years from 12 to 90, so we can take 78 and plug it into this wonderful equation seen below this nice smiley face. c:
years/(years until correct time)
78/11.8= approx. 6.6
And since a watch can't be correct 6.6 times, the answer is 6 times.
Yay. :))))))))
RWA-ish:
- Jeff probably should get a new watch soon because then he'll be late for all his meetings and this watch will render useless.
A good mathematician learns from their mistakes ccccccccccccc:
DeleteIndeed they do Fiona!
DeleteWait isn't the watch supposed to be good, not stopped? If it was good I don't think it would be correct every 12 hours(probably a much longer period of time).
ReplyDeleteI assumed this question meant that the watch would gain 10 seconds at the end of the day. So, it would be normal(ish) for the whole day, then when it reaches midnight of the next day, it would gain 10 seconds.
Deleteaaaaaaaaaaand i over thought the question :T
DeleteAaaaaaaand that'd right Oliver, I mean Jamin-Oliver-Jamin
DeleteGRADE 7/8 POTW
ReplyDeletethe solution to this POTW is quite simple. In my opinion, you have to find out how many seconds pass on the watch in 78 years and then divide by the number of seconds in 12 hours.
10 seconds= 1 day . 365 days x 10=3650= 1 year 3650 x 78= 284700= Number of seconds in 78 years
Number of Seconds in 12 hours= 60x60x12=43200 seconds in 12 hours
284700/43200= 6.6 Approx. 6.6 is not an integer so 6 is the answer.
The clock will show the correct time 6 times from the age of 12 to 90.
Maruti
ReplyDeleteSeconds in a day 60 x 60 x 24 = 86400
Since it gains 10 seconds divide that by 10 and it will take 8640 days to show the correct time.
There are 28468 days because the 12 and 90 birthdays are excluded.
Divide 28468 by 8640 equals 3.3 approximately but there is P.M. and A.M. so multiply it by 2 so you get 6.6.
Since you have to round down because there can't be extra days it will show the correct time 6 times from that time frame.
Done on paper 6 times
ReplyDeleteAnswer is 6 times
ReplyDeleteDone on paper
This comment has been removed by the author.
DeleteAliyah Meltz
ReplyDelete90-12=78 years
Since the watch gains ten seconds per day and there is 365 days per year then 365x10=3650. To find the amount of seconds in 78 years then you multiply 3650x78=284,700
Now since the watch will obviously be correct every 12 hours than since there are 43,200 seconds in 12 hours then 284,700/43,200=6.6
Because we must round 6.6 then the watch will show the correct time 6 times from Jeff's age 12-90.
90-12=78
ReplyDelete10 seconds every day
10*365.25=3652.5 seconds in a year
3652.5*78=284,895 seconds in 78 years
now divide this by the number of seconds in 12 hours (half a day)
12*60*60=43200
284,895/43,200
=it equals about 6 so based on that we can assume that it is only six times because it only hits the exact time 6 times it can't be 6 and 1 half or anything else.
I did it on paper and got 6 times.
ReplyDeleteGreat responsibility for continuing to record your answer here and your solution in your notebook.
DeleteThere are 365 days in a year, and we must multiply 10 and 365 to find how many seconds in a year. (3650) Then, we need to multiply by the remaining number of years until he reaches 90.
ReplyDeleteJeff's age= 12 Age required= 90 90-12=78
3650*78=255500+29200=284700
Based off what I know about clocks (I'm not an expert), every half day should count because the clock ticks 2 rotations in a day. The seconds in half a day are 12 hours*60*60=43200
We then divide 284700 by 43200 because that is the total time divided by the time taken for one correct rotation.
284700/43200 roughly equals 6.5, however, we still round down because half a tick does not count as a tick.
Therefore, the watch shows the correct time 6 times.
*le gasp*
Great! *le chirp*
Deletealso subcomment leap years probably don't do much
ReplyDeleteI tried factoring them in but it only added like a miniscule amount to the total
POTW:
ReplyDeleteFirst we need to figure out the amount of seconds in one year, if the watch gains 10 seconds every day: 365 x 10 = 3650.
He will turn 90 in 78 years, as 90 - 12 = 78
3650 x 78 = 284700.
Each day has 12 hours. There are 3600 seconds in every hour: 3600 x 12 = 43, 200
Now, we divide 284700 by 43, 200 giving us 6.590, rounded to 6.6, rounded to 6.
The clock will be right 6 times.
Seconds in a day 60 x 60 x 24 = 86400
ReplyDeleteThe watch gains 10 seconds each day, so you would divide that by 10 (8640) and it will take 8640 days to show the correct time.
There are 28470 days between the 12th and 90th birthdays
Divide 28468 by 8640 equals 3.3 approximately.
Since there is P.M. and A.M. you would have to multiply it by 2 so you get 6.6.
Since you have to round down because there can't be extra days added, it will show the correct time 6 times from when he is 12.
First find the number of second in a day 60*60*24=86400
ReplyDeleteThen you need to find how many days it will take for the watch to show the correct time which would be total seconds divided by 10. 8640 days
Then find the days in 78 years (90-12) 28468
Then divide and you get 3.3 for each 12 hours.
multiply by 2 for 1 day
6.6
then go down because you are counting the number of days and you can't have half a day.
6 times
Full sentence answer to the question posed please!
DeleteThe watch would gain 1 hour in 60*6 or 360 days, therefore it will gain 12 hours in 12*360= 4,320 days which is equal to 4,320/365 or around 11.8 years.
ReplyDeleteBetween the age of 12 and 90 there are 78 years, so 78/11.8=6.6, so it would have shown correct time 6 times by the time he is 90.
Great work
Delete