A new machine can make 12,500 aluminum cans four times faster than an older machine. With both machines working, 12,500 cans be made in 20 h. How long would it take the new machine, working alone, to make 12,500 cans?
A) 24 h
B) 25 h
C) 80 h
D) 27 h
E) 26 h

Question

Quizplus · Accepted Answer

Let's call the production rate of the older machine "r". Then, we know that the production rate of the new machine is 4r (four times faster).

Together, the two machines can produce 12,500 cans in 20 hours. This means that their combined production rate is:

12,500 cans ÷ 20 hours = 625 cans/hour

We can now set up an equation using this information:

r + 4r = 625

Simplifying, we get:

5r = 625

r = 125

So, the old machine can produce 125 cans per hour.

Now we can use the production rate of the new machine to figure out how long it would take it to produce 12,500 cans working alone:

4r = 4(125) = 500

12,500 cans ÷ 500 cans/hour = 25 hours

Therefore, the answer is B) 25 h.

A New Machine Can Make 12,500 Aluminum Cans Four Times