SOLUTION: Every time Stephen walks the dog on time he gets 30 minutes to play video or computer games. When he does not take out the dog on time he gets a mess to clean up or lose 1 hour of

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Question 1006378: Every time Stephen walks the dog on time he gets 30 minutes to play video or computer games. When he does not take out the dog on time he gets a mess to clean up or lose 1 hour of video or computer game time. this week he walks the dog on time 8 times more than he did not walk the dog on time. In total he has accumulated 3 hours of video or computer time. How many times has Stephen not walked the dog on time?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
from what i can see, stephen has not walked the dog on time at least 2 times.

here's why.

let x = the number of times he has walked the dog on time.

let y = the number of times he has not walked the dog on time.

you are given that x = y + 8

look at the following table: 



x           y          x * .5        y * 1      x - y
8           0          4             0          4
9           1          4.5           1          3.5
10          2          5             2          3            *****
11          3          5.5           3          2.5


if the only punishment is loss of video hours, the minimum number of hours he could have not walked the dog on time is 2.

when y = 2, x = 10
he gains 10 * .5 = 5 video hours and he loses 2 * 1 = 2 video hours for a net video hours of 3.

when y = 3, x = 11
he gains 11 * .5 = 5.5 vido hours and he loses 3 * 1 = 3 video hours for a net video hours of 2.5.

however !!!!!
he can be punished by loss of video hours or cleanup of mess hours.
if he loses 2.5 video hours and gets .5 cleanup hours, then his net video hours becomes 5.5 - 2.5 = 3.

so the option of cleanup time rather than loss of video time can make the net video hours equal to 3 for any number of not on time hours greater than or equal to 2.

the balance of the not on time hours is just punished by cleanup time instead of lost video time.

i did the analysis in an excel spreadsheet for multiple of not on time to show you the possible impact if you want to freeze the net video hours to 3.

that worksheet is shown below:

$$$

you analyze this worksheet as follows:

look at on time = 25 and not on time = 17 (row 21 in the worksheet).
25 * .5 = 12.5 hours of video time earned.
in order for the net video hours to be equal to 3, then 12.5 - 3 = 9.5 hours of lost video time must have been incurred.
the total hours of not on time is equal to 17.
17 hours minus 9.5 hours of lost video time = 7.5 hours left of not on time that is now punished by cleaning up the mess rather than lost video time.

what this says is that you can have net video hours of 3 for any number of not on time incidents as long as they are greater than or equal to 2.
you just punish the balance by giving cleaning up the mess hours rather than lost video time hours.

if the only option was lost video time hours, then the only solution sould have been 2 incidents of not on time with 10 incidents of on time.
that would have incurred 10 * .5 = 5 hours of video time hours earned minus 2 hours of video time taken away for a net of 3 video hours.