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

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Intern
Joined: 06 Sep 2012
Posts: 4
Location: United States
If Sally can paint a house in 4 hours, and John can paint  [#permalink]

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Updated on: 02 Nov 2012, 13:06
7
00:00

Difficulty:

5% (low)

Question Stats:

92% (01:04) correct 8% (01:46) wrong based on 375 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

Originally posted by MariaF on 02 Nov 2012, 09:46.
Last edited by Bunuel on 02 Nov 2012, 13:06, edited 1 time in total.
Renamed the topic and edited the question.
Intern
Joined: 05 Sep 2012
Posts: 1

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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.

Intern
Joined: 06 Sep 2012
Posts: 4
Location: United States

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02 Nov 2012, 10:25
1
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 :/
Manager
Joined: 25 Jun 2012
Posts: 63

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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?
Manager
Joined: 31 Oct 2012
Posts: 59
Schools: Mays '16, Simon '16

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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]
Manager
Joined: 25 Jun 2012
Posts: 63

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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
Joined: 31 Oct 2012
Posts: 59
Schools: Mays '16, Simon '16

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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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Posts: 426
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GPA: 3.23
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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Posts: 208
Location: United States
GPA: 3.4
Re: If Sally can paint a house in 4 hours, and John can paint  [#permalink]

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26 Jun 2017, 15:48
$$W=\frac{AB}{A+B}$$ 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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Posts: 3355
Re: If Sally can paint a house in 4 hours, and John can paint  [#permalink]

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26 Jun 2017, 17:18
Top Contributor
1
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

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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, 13:40
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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If Sally can paint a house in 4 hours, and John can paint  [#permalink]

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23 Sep 2018, 09:41
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 :/

When you have two people (or machines, or other entities) working together to complete a job, you can add their rates together to find their combined rate. Typically, as you see here, the information you are given will be in terms of time. To add the rates, you'll want to first convert times to rates.
If Sally can paint a house in 4 hours, and John can paint &nbs [#permalink] 23 Sep 2018, 09:41
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