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Question 158177: eight stock clerks can stock 26,000 cans in 10 hrs. How long will it take 5 such clerks to stock 16,250 cans?
Found 2 solutions by Edwin McCravy, gonzo:
Answer by Edwin McCravy(20081)   (Show Source):
You can put this solution on YOUR website! Eight stock clerks can stock 26,000 cans in 10 hrs. How long will it take 5 such clerks to stock 16,250 cans?
Without using algebra, just basic math. Were you supposed to
use algebra? If so post again or email me.
Rule:
If you start with this:
W workers can do J jobs in H hours.
Then if you multiply or divide any two of the quantities
W, J, and H each by any positive number, leaving the third
quantity as it is, then the resulting statement will be
true.
8 stock clerks can stock 26,000 cans in 10 hrs.
To see what 1 stock clerk can do, let's divide the quantities
8 and 26,000 by 8, leaving the 10 hours as it is:
1 stock clerks can stock 3250 cans in 10 hrs.
Now to see what 5 stock clerks can do, let's multiply the quantities
1 and 3250 by 5, leaving the 10 hours as it is.
5 stock clerks can stock 16,250 cans in 10 hrs.
Hey, we need go no further, because it just so happened that
that accidentally turned out to be the desired number, 16,250
cans. (That won't just happen in most problems, but it did
here!!)
So the answer is 10 hours.
Edwin
AnlytcPhil@aol.com
Answer by gonzo(654)  (Show Source):
You can put this solution on YOUR website! clerks * rate * time = units
clerks is number of stock clerks
rate is number of units stocked per hour per stock clerk
time is in hours.
units is number of cans stocked.
let s = number of stock clerks
let r = number of cans stocked per hour per clerk
let t = number of hours it took to complete the job
let c = number of cans stocked in total
formula becomes
s*r*t = c
r = c/h/s = cans stocked per hour per clerk = c/(h*s)
substituting in the first part of the problem,
s = 8
r = r (unknown at this time)
t = 10
c = 26000
equation is s*r*t = c
substituting in this equation we get
8*r*10 = 26000
solving for r, we get
r = 26000/(8*10) = 325 cans stocked per stock clerk per hour.
now that we know the rate, we can solve for the second part of the problem.
same equation is used, i.e. s*r*t = c
in this case, however,
s = 5
r = 325
t = t (unknown at this time)
c = 16250
substituting in the equation s*r*t = c
we get
5*325*t = 16250
solving for t, we get
t = 16250/(5*325) = 16250 / 1625 = 10
answer is t = 10 hours.
so 5 stock clerks working for 10 hours and stocking 325 cans per stock clerk per hour will stock 5*10*325 = 16250 cans.
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