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Question 844964: if two assemblers can assemble two toys in two minutes,how many assemblers would it take to assemble eight toys in six minutes?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 2 assemblers can assemble 2 toys in 2 minutes.
the basic formula to use is:
p * r * t = q
p is equal to the number of people who are working.
r is equal to the average rate of work per minute that each worker is performing at. the rate is assumed to be the same for each worker.
t is equal to the time in minutes.
q is equal to the quantity of work performed.
in this problem, we are given the following:
2 assemblers can assemble 2 toys in 2 minutes.
put this in the formula and we can solve for r, which is the average rate that each person works at.
the formula of:
p * r * t = q
becomes:
2 * r * 2 = 2
solve for r to get r = 1/2
each worker can assemble 1/2 of a toy in one minute.
now you want to know how many assemblers would it take to assemble 8 toys in 6 minutes.
the formula of:
p * r * t = q
becomes:
p * 1/2 * 6 = 8
solve for p to get p = 8/3
it would take 8/3 workers to assemble 8 toys in 6 minutes.
to confirm, replace p with 8/3 in the formula to get:
8/3 * 1/2 * 6 = 8
simplify to get:
8 = 8
this confirms that value of p is good.
if you need to round to a whole person, then the answer would be 3 people would be required.
in that case, the formula of p * r * t = q would become:
3 * 1/2 * 6 = q which would simplify to:
9 = q.
the 3 people would produce 9 toys in 6 minutes which is the smallest number of toys to be produced in 6 minutes if the workers are assembling toys at the average rate of 1/2 toy per person.
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