Question

One printing press can print 5,000 advertising cards in 12 seconds. Another printing press can print the same number of cards in 7 1/2 seconds. If both presses are used together to print the 5,000 cards, how many seconds will it take them?
Please answer ASAP.

Answer 1

I think it is the answer is    4.62

Tell me if its right

Answer 2

We first of all find the rate at which each of them print,

The first can print 5,000 cards in 12 seconds
So the rate of printing is
$= \frac{1}{12}$

The second can also print in 7½ seconds

So the rate of printing is
$= \frac{1}{7 \frac{1}{2} }$
$= \frac{1}{ \frac{15}{2} }$
$= \frac{2}{15}$


Now let the time taken by both to complete be t.

Then their combined rate
$= \frac{1}{t}$


So adding their individual rate should give us the combined rate.

That is

$\frac{1}{12} + \frac{2}{15} = \frac{1}{t}$

So we multiply through by the LCM which is
$60t$


This implies that

$\frac{60t}{12} + 60t \times \frac{2}{15} = \frac{ 60t }{t}$
$5t + 8t = 60$
$13t = 60$
$t = \frac{60}{13}$

Hence it will take them
$t = 4 \frac{8}{13} \: seconds$