If Sally can paint a house in 4 hours, and John can paint : GMAT Problem Solving (PS)
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# If Sally can paint a house in 4 hours, and John can paint

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Intern
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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, 09:46
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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, 13:06, edited 1 time in total.
Renamed the topic and edited the question.
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02 Nov 2012, 10:16
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, 10:25
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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, 12:11
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, 12:17
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, 12:22
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)?
Manager
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02 Nov 2012, 12:30
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, 03:13
$$\frac{1}{4}+\frac{1}{6}=\frac{10}{24}=\frac{5}{12}$$

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

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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, 11:35
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Re: If Sally can paint a house in 4 hours, and John can paint   [#permalink] 06 Jan 2016, 11:35
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