nerdy weed pickers

i am a nerd. and my sister is too--let me tell you why.

So we are employed at a farm just outside of Orange City called PUMPKINLAND! (Anne Randi...that was for you!) At this farm we are asked to pick the weeds that have grown up between the precious pumpkin plants. Christa has worked here last year quite a lot so she is sort of a self proclaimed site manager. It is just her and me so she is keeping me in line. She makes me do the weeds around the plants because she is irritated by the juice that emits from the pumpkin leaves. She is the weed nazi and the math wizz!

Ever since we started working there on Monday we have been on a search to solve a little algebra problem. We are both well out of our high school algebra days but we had a problem and we had to try to figure out the answer. So as we picked weeds we brainstormed, used her phone as a calculator, and dreamed up solutions to our curiosity.

Here is the senario that we spent many hours pondering.

So everyday when we come into the barn we CLOCK IN on the punch clock on the wall. We notice that the time clock sometimes says numbers that are not 'really' the time and that caught our attention. Us being equally and most intensely curious we wondered how that could be and perhaps it had something to do with our paycheck?? Maybe the punch clock is run on a 100 minute hour which would mean we would get paid a little over half of what we thought! OH NO! I have never heard of a 100 min hour....but it could be. No it can't be that....it has to be an hour otherwise the whole system would be screwed up just after midnight everyday....you see the punch clock turned 9:00 exactly when the wrist watch did. So we figured there must be a pattern to the strangeness. For example, we clock in at 8:06am and the punch card says 8.10. So how could it be off already?

Ok....so this is what we came up with. The punch clock runs on a digital 100 cycle. It also has a clock on it which tells the correct time on a digital 60 cycle (like normal). So how can 100 and 60 work together? How can I manage to punch in at 8:98 and someone is able to understand that??
Christa and I talked it through and presented ideas for dividing this and that....and finding the difference here and there. Tonight was our crowning moment when we tried making a line graph to measure the ticks (of the punch clock) compared to the minutes in an hour. To tell you the truth, we had the answer to our questions a long time before we understood it. Christa somehow got an answer of .36 or what we thought could be 36 sec=1 tic. That was a fluke.....but it was also our solution. The punch clock ticks every 36 seconds so that it can make it to the 100 mark at the same time as the minutes get to the 60 mark. WOW....as I tell this I just feel smart for working on this nerdy math problem and getting so much joy out of it!!

As I look at it now......in hind sight....we could have taken the ratio 100:60 and then found the highest common number. That would be 20. Take 100 / 20 and you get 5. Take 60 / 20 and you get 3. The ratio of ticks per minute is 5:3!!
We did not just find this answer....oh no...we did the line graph. I made the x axis and the y-axis and I put dots on the graph going up every .36 seconds from zero. We saw a pattern come forth when at 5 ticks.....it was 3 minutes. Christa freaked out and said....WAIT! There is something here.......and then we had it. That was it.....we got the pattern and now the mystery is solved.

The punch clock ticks every 36 seconds that way it can get to 100 by the time the clock gets to 60. We made a chart of numbers and dots...we think it will help us. (no....it's purely nerdy)

So if you want to do some math yourself just take the ratio equation 5:3=ticks:min.
you have to cross multiply. it is hard to express this on the computer but put 5ticks on top of 3minutes like a fraction and set that equalling the ticks your punch card said over the time in minutes. x is the number you are trying to find. you multiply across and opposite then divide.

EXAMPLE PROBLEMS:
1. Christa punches the card at 8.98 what time did she clock in?
You would take 5/3=(98 ticks)/x
WHAT IS X?
so since '5' and '98' are the same units you do not multiply or divide them together. you are trying to find x....which is minutes. you multiply 98 by 3 (across the equal sign and down (opposite)) and then you divide by 5.
X=58.5min
Christa punched in at 8.98 but the time was 8:58(.5sec)am

2. Erika is on her bike going home after work...she forgot to punch out for the day so she looks at her watch and sees it is 9:34pm. What number will she put on the card the next day...in order to be correct?
5ticks/3min= x ticks/34min what is x?
x=
(if you can figure it out....please post a comment)


THIS NEXT PROBLEM IS AN ACTUAL SENARIO:
3. Erika is going to participate in a missions debriefing program in Colorado Springs at the end of August. This program will be good for her to respond and move forward after spending 3 years in Norway. The program cost $745 dollars. $150 of the total has been taken care of by anonymous givers but that leaves $595 to raise. She gets paid $9 an hour to pick weeds and do math in the fields. If she rides her bike it is 3 miles out to Pumpkinland from her house.
1.How many hours does she have to work per day to spread it out before Aug 7?
2.How much money does she earn per tick?
3.How many miles does she rack up from riding her bike to work and back?


thank you for enjoying yet another educational blog by yours truly.
my cold sore is healing up incredibly.....and so is my heart!

goodnight!

rika