At a cafeteria, the automatic ice machine can completely fill itself in 20 minutes. During lunch time, customers can completely empty the ice machine in 30 minutes. At the start of lunch time, the ice machine is completely and it starts making ice at the same time that customers start taking ice. How long will it take for the machine to be completely full? (Hint: The customers take away the ice.)
a. 12 minutes. b. 30 minutes
c. 20 minutes. d. 60 minutes
I just answered a very similar question for you .
Notice that in the previous post I added the two rates.
In this case you would subtract one rate from the other.
See if you can follow the same method.
let me know what you get.
60
To solve this problem, we can break it down into smaller components and calculate the rate at which the ice machine and the customers work.
First, we need to find the rate at which the ice machine produces ice. We know that the machine can completely fill itself in 20 minutes, so its rate of production is 1 machine per 20 minutes, or 1/20 machines per minute.
Next, we need to find the rate at which the customers remove ice. We know that the customers can completely empty the ice machine in 30 minutes, so their rate of removal is 1 machine per 30 minutes, or 1/30 machines per minute.
Now, we can calculate the net rate at which the ice machine is being filled or emptied. Since the customers are removing the ice, the net rate is the difference between the rate of filling and the rate of emptying. Therefore,
Net rate = Rate of filling - Rate of emptying.
Substituting the values we calculated earlier, we get:
Net rate = 1/20 - 1/30
= 3/60 - 2/60
= 1/60 machines per minute.
This means that every minute, the ice machine is being filled at a rate of 1/60 machines.
Since the ice machine is initially completely full, and it takes 1/60 machines to fill it every minute, it will take a total of 60/1/60 = 60 minutes for the machine to be completely filled.
Therefore, the correct option is d. 60 minutes.