Question

A company has two large computers. The slower computer can send all the company's email in 45 minutes. The faster computer can complete the same job in 30 minutes. If both computers are working together, how long will it take them to do the job? Do not do any rounding.

Answer 1

The first computer's rate is 1/45 email jobs per minute, the second computer's rate is 1/30 email jobs per minute, so presumably they combine for a rate of

1/45 + 1/30 = 2/90 + 3/90 = 5/90 = 1/18 email jobs per minute, so both together do a full job in the reciprocal,

Answer: 18 minutes

Answer 2

Answer:

It will take both the computers 18 minutes to the job together.

Step-by-step explanation:

The slower computer can send all the company's email in 45 minutes.

The faster computer can complete the same job in 30 minutes.

Let they take 't' minutes to complete the task together.

As they are completing 1 job, we get the following equation:

$\frac{t}{45} +\frac{t}{30}=1$

LCM of 45 and 30 is :

45 = 3 x 3 x 5

30 = 2 x 3 x 5

LCM = 2 x 3 x 3 x 5 = 90

Now, solving for t;

$\frac{2t+3t}{90}=1$

=> $\frac{5t}{90}=1$

=> $5t=90$

Dividing both sides by 5;

$\frac{5t}{5} =\frac{90}{5}$

We get t = 18

Hence, it will take both the computers 18 minutes to the job together.