computers working together to complete operations

jmedsy · #1 $Old$ November 2nd, 2009, 06:34 PM

If:

Computer A takes 4 hours to complete a set of operations,
and computer B takes 2 hours to complete the same set of operations,

how long does it take for both computers A and B working together to complete the same set of operations?

I'm having a hard time putting this into algebra. I arrived at numerous improper fractions and ultimately settled on "1 hour," but that doesn't seem right. Could somebody walk me through this?

Gusbob · #2 $Old$ November 2nd, 2009, 06:44 PM

Let the total work required to complete the operation = x units of work

Computer A takes 4 hours to complete x. The rate it runs the operation is x/4 units of work per hour.

Computer B takes 2 hours to complete x. The rate it runs the operation is x/2 units of work per hour.

You are trying to find the time (lets call it 't') it takes for both of them working together to complete x.

So their combined rate of work x t = combined work done.

$(\frac{x}{4} + \frac{x}{2}) t = x$

Now you can solve for t. The x variable cancels out.

jmedsy · #3 $Old$ November 2nd, 2009, 08:11 PM

looks good, thanks