Question

there are two machines that produce aluminum cans. the newer machine can produce 5700 cans in 190 minutes. it takes the older machine 285 minutes to produce that many cans. if the two machines work together, how long will it take them to produce 5700 cans?

Explanation:

Step1: Calculate the rate of the newer machine

The rate of the newer machine is $\frac{5700}{190}=30$ cans per minute.

Step2: Calculate the rate of the older machine

The rate of the older machine is $\frac{5700}{285}=20$ cans per minute.

Step3: Calculate the combined rate

The combined rate of the two machines is $30 + 20=50$ cans per minute.

Step4: Calculate the time taken to produce 5700 cans together

The time $t=\frac{5700}{50}=114$ minutes.

Answer:

114