Word prob: If Sally can paint a house in four hours....

wallee

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If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together? do i add and then divide by 2?
 
Re: Word prob -basic alg

wallee said:
If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together? do i add and then divide by 2?
Put on your thinking cap, wallee... if you add then divide by 2, you get 5:
but Sally can do it in 4; so if she gets help from John, it sure won't take 5 hours, right?

Hint: in 1 hour, Sally paints 1/4 if the house...kapish?
 
wallee said:
do i add and then divide by 2?

6 divided by 4=1.5??

6-4=2 hours?
Unfortunately, randomly guessing is unlikely to work on the tests. So instead, try using the techniques you were taught in your book and / or in your class. To review, try studying some lessons online:

. . . . .Google results for "work word problems"

Read at least two lessons from the link above, after having reviewed the relevant section(s) of your book and notes. Then please attempt this exercise again. If you get stuck, please reply with a clear listing of your work and reasoning, starting with the variables you picked and how you defined them.

Thank you! :D

Eliz.
 
This what is called a "joint effort" problem. This type of problem is usually best solved by considering what happens in one unit of time. In this case the unit of time is an hour. One of them can do the entire job in 4 hours, so in one hour 1/4 of the job is done. The other can do the job in 6 hours so in one hour he/she can do 1/6 of the entire job. If we let x represent the time it takes for them to do the entire job when working together, then in one hour they can do 1/x of the job.
Enough hints, already. Now, you put that all together and build your equation on the basis of what happens in one hour and solve for x.
 
If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together? do i add and then divide by 2?

<< If it takes me 5 hours to paint a room and you 3 hours, how long will it take to paint it together? >>

Method 1:

1--A can paint the house in 5 hours.
2--B can paint the house in 3 hours.
3--A's rate of painting is 1 house per A hours (5 hours) or 1/A (1/5) houses/hour.
4--B's rate of painting is 1 house per B hours (3 hours) or 1/B (1/3) houses/hour.
5--Their combined rate of painting is 1/A + 1/B (1/5 + 1/3) = (A+B)/AB (8/15) houses /hour.
6--Therefore, the time required for both of them to paint the 1 house is 1 house/(A+B)/AB houses/hour = AB/(A+B) = 5(3)/(5+3) = 15/8 hours = 1 hour-52.5 minutes.

Note - T = AB/(A + B), where AB/(A + B) is one half the harmonic mean of the individual times, A and B.

I think this should give you enough of a clue as to how to solve your particular problem.
 
ok thanks. So let me try 1/4+1/6=1 then I need 24 as my denominator so I can add so that gives me 6/24x +4/24x=24, so then I get10x=24, divide both sides by 10 and I get 2.4???is this it?
 
>ok thanks. So let me try 1/4+1/6=1 then I need 24 as my denominator so I can add so that gives me 6/24x +4/24x=24, so then I get10x=24, divide both sides by 10 and I get 2.4???is this it?

1/4+1/6=1 should be 1/4+1/6=1/x

6/24x +4/24x=24 should be 6/24x +4/24x=1 or 6/24x +4/24x=24/24

Next step, multiply both sides by 24 ... 6x + 4x = 24

so then I get10x=24 >>> Yes. x=2.4 hours which is 3 hours and ??? minutes?

You seem to be having the correct thought process. As I see it, you are careless about being precise which will probably lead to small errors that will produce the wrong answer. I encourage you to refrain from taking short cuts so that you won't make those little errors. It will pay you off in the long run. Forgive me for preaching.
 
So let me try 1/4+1/6=1 then I need 24 as my denominator so I can add so that gives me 6/24x +4/24x=24, so then I get10x=24, divide both sides by 10 and I get 2.4???is this it?

T = 4(6)/(4 + 6) = 24/10 = 2.4 hours.

Right on!!!
 
Wallee. This is what I was talking about when I said you need to be more specific. You make the statement...

"So let me try 1/4+1/6=1 then..."

And then the next poster said "Right on." which may lead you to think that you can be sloppy in math and nothing bad will happen. In this case you are right. However, look at the above statement. Is 1/4+1/6=1? Certainly, your teacher will take exception to that statement as will everyone else who sees it, and that kind of sloppiness will eventually backfire on you. 'Nuff said.
 
Keep that attitude wallee, and you'll end up flipping burgers at Burger King,
working your way up to Flipper Supervisor...
 
with a 4.0 my first semester at UCLA, I dont think I will be working any fast food places anytime soon....
 
wallee said:
with a 4.0 my first semester at UCLA, I dont think I will be working any fast food places anytime soon....
If that's the truth, then sincere apologies...
BUT why do you post grade 5 problems like:
"A pair of skates normally cost 110.99. They are in sale 10% off. What is the price after the discount.

I am bad with percentages and I get confused. I mult. the original price times 10 then divided by 100 and I got 99 for my answer which is completely wrong. Please help."

Are you pulling our legs?
 
I am not an expert at math, but I volunteer as a tutor when I have time. I have never been a math person but I am really trying to understand it...it's not as bad as I thought.
 
wallee said:
full time I tutor when I can
You're a full-time tutor at UCLA, but you can't do grade-school arithmetic...? :shock:

That seems... implausible.... :?

Eliz.
 
Ya...agree Eliz. Looks like wallee is a legion in his own mind.
Like, how can one be enrolled at UCLA, yet can't work out a simple discount :shock:
 
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