Anew machine makes 20,000 aluminum cans three times faster than an older machine. with both machines operating, it takes 15 h to make 20,000 cans. how long would it take the new machine, working alone, to make 20,000 cans?

New machine, working alone will take 20 hours to complete 20000 aluminium cans.

Solution:

For sake of simplicity let’s assume new machine be Machine “N” and old machine be Machine “O”

Let’s assume cans manufacture by machine “O” in 1 hour = x  

Since machine N is three times faster than “O”,

So cans manufacture by machine N in 1 hour = 3x  

Cans manufactured in 1 hour when both machines are operating simultaneously  is equal to cans manufacture by machine O in 1 hour + cans manufacture by machine N in 1 hour

That is cans manufactured in 1 hour when both machines are operating = x + 3x = 4x

So cans manufactured in 15 hours when both machines are operating =

Given that cans manufactured in 15 hours when both machines are operating = 20000

60x = 20000  

3x = 1000 cans  

As cans manufacture by machine N in 1 hour = 3x = 1000

So number of hours required by machine N to produce 1000 cans alone = 1 hour

So number of hours required by machine N to produce 1 can alone = hours

And number of hours required by machine N to produce 20000 cans = = 20 hours

Hence new machine, working alone will take 20 hours to complete 20000 cans.