SOLUTION: A new machine makes 20,000 aluminum cans three times faster than an older machine. With both machines operating, it takes 6 h to make 20,000 cans. How long would it take the new ma

Question 1124934: A new machine makes 20,000 aluminum cans three times faster than an older machine. With both machines operating, it takes 6 h to make 20,000 cans. How long would it take the new machine, working alone, to make 20,000 cans?
Found 5 solutions by josgarithmetic, Theo, ikleyn, MathTherapy, Alan3354:
Answer by josgarithmetic(39629)   (Show Source): You can put this solution on YOUR website!
One job is "make 20000 aluminum cans".

Rate for old machine, r
Rate for new machine, 3r

Both machines together take 6 hours to do 1 job.

-
Question is asking for reciprocal of .

---------------eight hours for new machine to do 1 job working alone.
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
rate * time = quantity of work produced.

the rate of the new machine is 3 times the rate of the old machine.

if the rate of the old machine is x, then the rate of the new machine is 3x.

when both machines work together, their rates are additive.

therefore:

(x + 3x) * time = quantity of work produced.

time is 6 hours and quantity of work produced is 20,000, therefore:

(x + 3x) * 6 = 20,000.

combine like terms to get 4x * 6 = 20,000

\divide both both sides of the equation by 24 to get:

x = 20,000 / 24 = 833 and 1/3.

3x is therefore 3 * (833 + 1/3) = 2500

to see if these rates are accurate, replace x and 3x in the original equation to see if it holds truel.

the original equation is (x + 3x) * 6 = 20,000.

substituting 833 and 1/3 for x and 2500 for 3x, we get:

((833 + 1/3) + 2500) * 6 = 25,000.

this results in 25,000 = 25,000, which is true, therefore you can assume that the rates are accurate.

given that the rate of the new machbine is 2500 aluminum cans per hour, then the formula for the new machine is 2500 * time = 20,000.

this results in time = 20,000 / 2500 = 8 hours.

the new machine would take 8 hours working alone.

breaking down the 6 hours when working together, you get:

(833 + 1/3) * 6 = 5000 aluminum cans in 6 hours.

2500 * 6 = 15000 aluminum cans in 6 hours.

total for 6 hours = 20,000 cans.

the new machine, at 3 times the rate of the old machine, produced 3 times the number of cans in the same 6 hours.

your solution is that the new machine would take 8 hours to make 20,000 aluminum cans, working alone.

Answer by ikleyn(52873)   (Show Source): You can put this solution on YOUR website!
.

When the faster machine works together with the slower machine, it is the same as if 4 slower machines work simultaneously. So, then we know that 4 slower machine do the job in 6 hours, working together. It means that one slower machine will complete the job in 4*6 = 24 hours. Since the faster machine works three times faster, it needs only 24/3 = 8 hours.

This problem can be solved mentally without using any equations, based only on your common sense.

Answer by MathTherapy(10556)   (Show Source): You can put this solution on YOUR website!

A new machine makes 20,000 aluminum cans three times faster than an older machine. With both machines operating, it takes 6 h to make 20,000 cans. How long would it take the new machine, working alone, to make 20,000 cans?

It's 1 job and that 1 job is making 20,000 cans
Let time newer machine takes be N
Then we get the following equation: OR
Solve any of the above and you should get a value of 8 for N, the time the new machine takes to do the ONE (1) job, alone!
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Is it 3 times faster?
Or 3 times as fast?

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