Question

A new 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?

Answer 1

Answer:

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 = $15 \times 4x = 60x$

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

60x = 20000  

$3x \times 20 = 20000$

$3x = \frac{20000}{20}$

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 = $\frac{1}{1000}$ hours

And number of hours required by machine N to produce 20000 cans = $20000 \times \frac{1}{1000}$ = 20 hours

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