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# If Sally can paint a house in 4 hours, and John can paint

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If Sally can paint a house in 4 hours, and John can paint [#permalink]

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02 Nov 2012, 10:46
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Question Stats:

94% (00:46) correct 6% (01:00) wrong based on 264 sessions

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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?

A. 2 hours and 24 minutes
B. 3 hours and 12 minutes
C. 3 hours and 44 minutes
D. 4 hours and 10 minutes
E. 4 hours and 33 minutes
[Reveal] Spoiler: OA

Last edited by Bunuel on 02 Nov 2012, 14:06, edited 1 time in total.
Renamed the topic and edited the question.

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02 Nov 2012, 11:16
Hello...

Sally can paint a house in 4 hours; Which means in 1 hour she can paint 1/4th of the house.
John can paint the same house in 6 hours. Which means in 1 hour she can paint 1/6th of the house.

Together in 1 hour they can paint: - 1/4 + 1/6 = 5/12th of the house.

Total Hours for painting the house together will be 12/5 = 2.4 Hours.

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02 Nov 2012, 11:25
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shrinivas280390 wrote:
Hello...

Sally can paint a house in 4 hours; Which means in 1 hour she can paint 1/4th of the house.
John can paint the same house in 6 hours. Which means in 1 hour she can paint 1/6th of the house.

Together in 1 hour they can paint: - 1/4 + 1/6 = 5/12th of the house.

Total Hours for painting the house together will be 12/5 = 2.4 Hours.

Thanks a lot I really made a stupid mistake :/

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02 Nov 2012, 13:11
MariaF wrote:
shrinivas280390 wrote:
Hello...

Sally can paint a house in 4 hours; Which means in 1 hour she can paint 1/4th of the house.
John can paint the same house in 6 hours. Which means in 1 hour she can paint 1/6th of the house.

Together in 1 hour they can paint: - 1/4 + 1/6 = 5/12th of the house.

Total Hours for painting the house together will be 12/5 = 2.4 Hours.

Thanks a lot I really made a stupid mistake :/

It'd be interesting how to use elimination techniques solving this problem?

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02 Nov 2012, 13:17
MariaF wrote:
Guys, help me please to solve this easy problem. I think I just make a stupid mistake
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?

A. 2 hours and 24 minutes
B. 3 hours and 12 minutes
C. 3 hours and 44 minutes
D. 4 hours and 10 minutes
E. 4 hours and 33 minutes

Time taken will be = x*y/x+y = 4*6/4+6 [ A]

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02 Nov 2012, 13:22
RJSPO wrote:
MariaF wrote:
Guys, help me please to solve this easy problem. I think I just make a stupid mistake
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?

A. 2 hours and 24 minutes
B. 3 hours and 12 minutes
C. 3 hours and 44 minutes
D. 4 hours and 10 minutes
E. 4 hours and 33 minutes

Time taken will be = x*y/x+y = 4*6/4+6 [ A]

Nice trick, I have to remember it, x*y/(x+y)
and if it would be three workers is it equal x*y*z/(x+y+z)?

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02 Nov 2012, 13:30
RJSPO wrote:
MariaF wrote:
Guys, help me please to solve this easy problem. I think I just make a stupid mistake
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?

A. 2 hours and 24 minutes
B. 3 hours and 12 minutes
C. 3 hours and 44 minutes
D. 4 hours and 10 minutes
E. 4 hours and 33 minutes

Time taken will be = x*y/x+y = 4*6/4+6 [ A]

Nice trick, I have to remember it, x*y/(x+y)
and if it would be three workers is it equal x*y*z/(x+y+z)?

No, for 3 workers it will be quite a complicated formula : x*y*z/xy+yz+zx
Better to use reciprocal formula for other cases

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Re: If Sally can paint a house in 4 hours, and John can paint [#permalink]

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14 Nov 2012, 04:13
$$\frac{1}{4}+\frac{1}{6}=\frac{10}{24}=\frac{5}{12}$$

$$Rt=W -> \frac{5houses}{12hrs}xt=1$$
$$t=\frac{12}{5}=2\frac{2}{5}hours=2 hours and 24 minutes$$

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Re: If Sally can paint a house in 4 hours, and John can paint [#permalink]

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06 Jan 2016, 12:35
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Re: If Sally can paint a house in 4 hours, and John can paint [#permalink]

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26 Jun 2017, 16:48
$$W=\frac{AB}{A+B}$$ where A and B are rates and W is the work done.

A=4; B=6
$$W=\frac{24}{10}$$

To convert to minutes $$= \frac{24}{10}*60 = 144$$ minutes
120+24 minutes , i.e 2 hours and 24 mins
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Re: If Sally can paint a house in 4 hours, and John can paint [#permalink]

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26 Jun 2017, 18:18
Expert's post
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1
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MariaF wrote:
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?

A. 2 hours and 24 minutes
B. 3 hours and 12 minutes
C. 3 hours and 44 minutes
D. 4 hours and 10 minutes
E. 4 hours and 33 minutes

We can solve this question quickly by using a little number sense.

Sally can paint a house in 4 hours
So, if there were TWO Sallys, they'd be able to paint the house in HALF the time.
In other words, TWO Sallys could paint the house in 2 hours

John can paint the same house in 6 hours
So, if there were TWO Johns, they'd be able to paint the house in HALF the time.
In other words, TWO Johns could paint the house in 3 hours

So, the time it takes Sally and John to paint the house will be BETWEEN 2 hours and 3 hours

This allows us to eliminate B, C, D, and E

[Reveal] Spoiler:
A

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Re: If Sally can paint a house in 4 hours, and John can paint [#permalink]

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27 Jun 2017, 14:40
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?

Work Done Together =

$$\frac{ab}{a + b}$$

$$= \frac{4 * 6}{4 + 6}$$

$$= \frac{24}{10}$$

= 2.4 Hrs

= 2 Hours 60 * 0.4 Min

= 2 Hrs 24 Mins

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Re: If Sally can paint a house in 4 hours, and John can paint   [#permalink] 27 Jun 2017, 14:40
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