Question

There are two machines that produce aluminum cans. The newer machine can produce 4200 cans in 210 minutes. It take the older machine 280 minutes to produce that many cans. If the two machines work together, how long will it take them to produce 4200 cans?

Answer 1

120 minutes or 2 hours

Explanation:

Proportions

The method to solve the problem is to compute how many cans produce each machine per minute, then add them to obtain the total cans produced by both. Finally, we compute the time to produce 4200 cans at that level of production.

The newer machine produces 4200 cans in 210 minutes, it means it produces

`\displaystyle (4200)/(210)`

=20 cans per minute

The older machine needs 280 minutes to produce the same 4200 cans, to it produces

`\displaystyle (4200)/(280)`

= 15 cans per minute

Together, they produce 20+15=35 cans per minute. Thus, to produce 4200 cans, they need

`\displaystyle (4200)/(35)`

= 120 minutes or 2 hours