SOLUTION: An old-model machine can stamp 1000 parts in 4 hours. A new-model machine can stamp 1000 parts in just two hours. How long will it take both machines to stamp 1000 parts working to

Question 75818: An old-model machine can stamp 1000 parts in 4 hours. A new-model machine can stamp 1000 parts in just two hours. How long will it take both machines to stamp 1000 parts working together?
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
One way to look at this problem is to determine the hourly rate of stamping parts for each
of the machines.
.
The old machine stamps out 1000 parts in 4 hours. That means that each hour it stamps
out 250 parts (1000 divided by 4). The new machine stamps out 1000 parts in 2 hours and
that means that it stamps at the rate of 500 parts per hour (1000 divided by 2).
.
If t represents the time that both machines are stamping together, then we just multiply
the rates of the two machines by t to get the output, and we need that output to be 1000 parts.
.
Does this make sense to you? Think of it this way ... if the machines work together for
one hour, the old machine produces 250 parts and the new machine produces 500 parts.
So together they have produced 750 parts. But we need 1000 parts. Suppose we let the
two machines work together for 2 hours. The old machine produces 250*2 or 500 parts and
the new machine produces 500*2 = 1000 parts. So in the 2 hours the combined output of
the two machines is 1500 parts ... more than we need.
.
The way to find the exact time needed is to multiply the unknown time, t, by each of
the rates of the two machines and set the answer equal to 1000. In equation form this
becomes:
.

.
Add the two terms on the left and you get:
.

.
Now divide both sides by 750 to find that:
.

.
So the production time to produce 1000 parts is 1.333333 hrs or 1 hr and 20 minutes
(a third of an hour is 20 minutes).
.
Hope this helps you to understand a little better a method for working work-rates
problems.
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