gbosl wrote:
Would you mind going through your line of thought on this. I do not understand why everything is 1/e, 1/f, 1/4, etc... why isn't it just e, f, 4, etc? Please help!!! Thanks
Let me try to explain based on my understanding:
e is the time that it takes an elf to build the treehouse
Hence, 1/e is the rate or speed of work for an elf (for eg. if it takes 8 hours for an elf to build the treehouse, the rate of work for the elf is 1/8th of the treehouse per hour)
Similarly, 1/f and 1/s are the RATES of work that a fairy and smurf can get done in an hour.
The equations represent the rate of work on both sides. For instance,
(1/s) + (1/e) = (1/2)
represents that in an hour, a smurf and elf together can build half the treehouse (think of 1/2 as -- if the total treehouse is 1, the RATE or speed of construction is 1/2 per hour)
Think of it as a speed, time and distance relationship. Rates can be added on both sides of the equation, as long as the distance is constant, and the time slice is fixed (per hour). Here the distance = 1 and the time we set the equations up for is 1 hour. So this would look like
[speed of construction for an elf] + [speed of construction for a smurf] = [their combined speed]
[total distance / time taken by an elf] + [total distance / time taken by an smurf] = [total distance / total time taken by an elf and smurf]
Hope that helps!