SOLUTION: If 5 men can manufacture 27 baskets in an hour, how many baskets would 15 men manufacture in 40 minutes?

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Question 1130086: If 5 men can manufacture 27 baskets in an hour, how many baskets would 15 men
manufacture in 40 minutes?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
n men
r rate per man
t time in hours
w amount of work, number of baskets

nr%2At=w


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5 men can manufacture 27 baskets in an hour,
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5r=27


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how many baskets would 15 men
manufacture in 40 minutes?
--
(40 minutes is 2%2F3hour .)
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15r%2A%282%2F3%29=w


w=15%2827%2F5%29%2A%282%2F3%29
.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Use the proportion


27%2F%285%2A1%29 = x%2F%2815%2A%28%282%2F3%29%29%29.     (*)


In this proportion,  2%2F3 represent 40 minutes as  2%2F3  of an hour,

and the proportion itself says that the rate of job of each man in one hour is the same in both cases.


Simplify (*)


27%2F5 = %283x%29%2F%2815%2A2%29,   or   27%2F5 = x%2F10,


and then get final answer  x =  %2827%2A10%29%2F5 = 27*2 = 54.     ANSWER

Solved.


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The proportion method shown by tutor @ilkeyn and the formula method shown by tutor @josgarithmetic are both good methods for solving problems like this.

My personal preference (what is easiest for me) is to consider how the number of baskets changes for each change in the parameters.

(NOTE: It will be good to understand and be able to use all three methods; for a particular problem, any one of the three might be the easiest to use.)

In this problem....

(1) The number of men increases from 5 to 15, an increase by a factor of 3; this will cause the number of baskets produced to increase by a factor of 3.
(2) The amount of time decreases from 1 hour (60 minutes) to 40 minutes, a decrease by a factor of 2/3; this will cause the number of baskets produced to decrease by a factor of 2/3.

So the number of baskets produced by 5 men in 1 hour (27), will get increased by a factor of 3 and decreased by a factor of 2/3:

(27)(3)(2/3) = 54.

ANSWER: 15 men in 40 minutes can produce 54 baskets.