Struggling with a math problem

I have been looking at the online practise sources for the NET, and am absolutely stumped by one particular type of math problem. Here's an example:

"Sally can paint a house in 4 hours. Bob can paint a house in 7 hours. How long will they take to paint the house together?"

I know there has got to be some kind of formula for solving this, but just can't figure it out. I need a more reliable method than "guesstimating".

Anybody here know how to solve this kind of problem?

Wouldn't you take the average, add both and divide by 2?

Doubting my math skills myself it's probbly not that easy and a very smart person will set this straight :)

Stpauligirl, I also thought you would just average the two numbers, but the correct answer (according to the NET practise site) is 2 hours and 24 minutes.

Any more ideas?

Edited to add-

The numbers in my first post were wrong, so I edited them to read Sally-4 hours, Bob-6 hours (not 7).

3/12 + 2/12 = 1/x .........12 is your common denominator 1/4 is equal to 3/12,

1/6 is equal to 2/12

5/12 = 1/x

x = 12/5 hours

12/5 hours X 60 mins/hr =

144 mins

Stpauligirl, I also thought you would just average the two numbers, but the correct answer (according to the NET practise site) is 2 hours and 24 minutes.

If you average the two numbers, you get 5 hours - longer than it would take Sally by herself! Maybe Bob is annoying the *$#*$^ out of her, hehehe.

You take the inverse of each number (like hrtprncss showed) and add them together to get x. The inverse of x is the correct answer.

Or, using a calculator:

4 hours = 1/4 = 0.25

6 hours = 1/6 = 0.167

---------------------

x = 0.417

1/x = 1/0.417 = 2.4 hours = 2 hours, 24 minutes

This solution will work no matter how many painters you have.

I'm still wondering why Sally and Bob would paint a house by themselves. :chuckle

Actually, I don't remember questions like this being on the NET. Does anyone else?

Good luck to you! :)

The online practice sources that I found were way more difficult than the actual test. The most reliable guide that I found that mirrored the NET was the NET study guide book put out by the educational resources folks (the book is mentioned on another thread in this forum, I believe).

The most difficult math you will encounter on the NET is very, very basic algebra (example: solve for x and the equation will be something like 2x + 7 = 31). Or something like a problem with multiple exponents and you will have to say which term is raised to the highest power.

Goodluck and don't stress too much, it's really not that bad of a test. :)

Exactly......

+, -, x, /, fractions, basic algebra, ratios

The NET Study Guide was great. (Bought mine on Ebay.)

purplemath.com is a great website for algebra problems.

Here's the page that explains how to do the painting problem:

http://purplemath.com/modules/workprob.htm

Thanks so much for all the replies and help.

I think I understand the problem now, but am even more relieved to hear that the NET isn't that bad.

I got a 24 on the math section of the ACT and felt like I could handle the NET, but when I saw those practise questions I just about flipped out!

Will definitely get the NET practise book.