Suppose Jonathan takes x hours to build 1 shed
Then Jonathan's shed-building rate is 1 shed per x hours.
That's or
Jonathan and Jose could build a shed, working together, in 6 1/2 hours;
So their combined shed-building rate is 1 shed per hours.
That's hours
That's or or
So their combined rate is 2/13:
but Jonathan worked alone for 3 hours
So using RATE × TIME = PRODUCTION (IN FRACTION OF A FENCE)
= = Jonathon's production as part of a
fence during the first 3 hours.
There was still 1 fence MINUS the part of the fence (3/x) which
Jonathon finished during the first 3 hours. That's the fraction
of a fence
left to be built.
and was then joined by Jose,
Therefore their rate was the combined rate of 2/13 of a fence per hour.
after which they finished the shed in 5 hours.
So using RATE × TIME = PRODUCTION (IN FRACTION OF A FENCE)
So Jonathon could build a shed by himself in 13 hours,
so his shed-building rate is
or
and since he worked a total of 3+5 or 8 hours, the
fraction of the fence Jonathan built was of the fence.
Therefore Jose built the remaining of the fence.
If they were paid in proportion to what the amount of work each accomplished, how should $96 be divided between them?
So Jonathon was paid times $96 or $59.08 and
Jose was paid times $96 or $36.92.
Edwin