Sam can paint the house in 8 days by himself, while Betty can paint the same house in 56 days. How long would it take Sam and Betty to paint the house together?

Question

Sam can paint the house in 8 days by himself, while Betty can paint the same house in 56 days.   How long would it take Sam and Betty to paint the house together?

parthkohli · Answer

If one dude can do a work in $x$, and the second can do it in $y$, then both do it in$$\dfrac{1}{x} +{\dfrac{1}{y}}$$

hero · Answer

Let 
S = the number of days Sam can paint a house alone
B = the number of days Betty can paint a house alone

Then together, they can paint the house in $\large\frac{S \times B}{S + B}$ days

hero · Answer

So in essence, compute:

$$\frac{8 \times 56}{8 + 56}$$

hero · Answer

@dumbsearch2, did you figure it out?

dumbsearch2 · Answer

112, right? (btw thanks for helping. :))

hero · Answer

No that's not right. Did you compute that by hand or calculator?

dumbsearch2 · Answer

calculator. :)

dumbsearch2 · Answer

and it says 112! :| with what you provided...

hero · Answer

You're inputting it into the calculator wrong.

hero · Answer

Maybe you'll understand what to do if I wrote it this way:

(8 × 56) ÷ (8 + 56)

Order of operations is important, especially with a calculator.

dumbsearch2 · Answer

youre right! :) the answer is 7?

hero · Answer

Exactly

dumbsearch2 · Answer

your so smart! :)

dumbsearch2 · Answer

thx for your help! :)

hero · Answer

You need to learn how to use a calculator bro.

hero · Answer

Or else you're going to get all your homework wrong.

dumbsearch2 · Answer

Yeah I should have done the Order of Operations, I usually do that, don't know what's wrong with me! :| I usually do please excuse my dear aunt sally: http://www.webquest.hawaii.edu/kahihi/mathdictionary/images/PEMDAS.png :) well thanks for your help! :)

dumbsearch2 · Answer

so like positive 7 right? :)

hero · Answer

Yes, bro. I already said it was correct.

hero · Answer

My only thing is, if you use a calculator, you have to know how to interpret what 

$\large\frac{a \times b}{a + b}$ means

hero · Answer

Because when you see that, you must understand that it means to do the operations in the numerator and the denominator first before dividing.

hero · Answer

when you see that, dividing will be your final step.

dumbsearch2 · Answer

right like in parenthesis right? like (axb)/(a+b) no?

hero · Answer

Exactly

hero · Answer

So $\large\frac{a \times b}{a + b}$ implies that $\large\frac{(a \times b)}{(a + b)}$

hero · Answer

I'm sorry that your teacher neglected to tell you that.

dumbsearch2 · Answer

ok. :)

anonymous · Answer

but the big division line bar also tells you that.  or realizing that "a + b" is the denominator, it would never make sense to separate them in a computation. or, etc. etc. etc.

hero · Answer

I know @binarymimic, but I was just providing some meaningful clarification for the poor guy.

anonymous · Answer

you're so kind

dumbsearch2 · Answer

thanks so much! :)