Question 1054139
assuming that these operate 24 hours a day and that there are 7 days in a week, then the total number of hours each is up, if they are up 100% of the time, will be 7 * 24 = 168 hours.


based on that assumption.


85% of the time will be .85 * 168 = 142.8 hours.
95% of the time will be .95 * 168 = 159.6 hours.


the general formula is rate * time = quantity of work produced.


the quantity of work produces is in kilowatt hours.
the time is in hours.
the rate will be in kilowatt hours per hour.


let w = the rate of the wind generator.
let h = the rate of the hydro unit.


for the first week, you get:


142.8 * w + 168 * h = 5880


for the second week, you get:


159.6 * w + (168 - 7.5) * h = 6240.


this can be simplified to 159.6 * w + 160.5 * h = 6240


you have 2 equations that need to be solved simultaneously.


they are:


142.8 * w + 168 * h = 5880
159.6 * w + 160.5 * h = 6240


assuming that you know how to solve equations simultaneously, i'll jump to the answer to tell you that the simultaneous solution to these equation is:


w = 26.86084142 kilowatts per hour.
h = 12.16828479 kilowatts per hour.


your solution is that the wind generator generates 27 kilowatts per hour and the hydro unit generates 12 kilowatts per hour.


i also solved this graphically as shown below.
look for the intersection between the lines of the two equations.
the coordinate point of the intersection confirms the solution.
in the graph, x represents w and y represents h.


<img src = "http://theo.x10hosting.com/2016/102405.jpg" alt="$$$" </>


you can confirm the solution is correct, by replacing w with 26.86084142 and h with 12.16828479 in the following equations.


142.8 * w + 168 * h = 5880
159.6 * w + 160.5 * h = 6240


if my assumptions about the number of hours in a week being equal to 168, then i believe this solution is correct.


check it out and see if you think that this is reasonable.