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If Sally can paint a house in 4 hours, and John can paint the same hou

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MariaF
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If Sally can paint a house in 4 hours, and John can paint the same hou [#permalink] New post   Updated on: 18 Feb 2019, 05:35
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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
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A

Originally posted by MariaF on 02 Nov 2012, 10:46.
Last edited by Bunuel on 18 Feb 2019, 05:35, edited 2 times in total.
Renamed the topic and edited the question.
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If Sally can paint a house in 4 hours, and John can paint the same hou [#permalink] New post   Updated on: 02 Apr 2020, 07:55
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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

Answer:
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A

Originally posted by BrentGMATPrepNow on 26 Jun 2017, 18:18.
Last edited by BrentGMATPrepNow on 02 Apr 2020, 07:55, edited 1 time in total.
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shrinivas280390
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Re: If Sally can paint a house in 4 hours, and John can paint the same hou [#permalink] New post   02 Nov 2012, 11:16
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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.

Hence Answer A
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Re: If Sally can paint a house in 4 hours, and John can paint the same hou [#permalink] New post   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.

Hence Answer A


Thanks a lot :) I really made a stupid mistake :/
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Re: If Sally can paint a house in 4 hours, and John can paint the same hou [#permalink] New post   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.

Hence Answer A


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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Re: If Sally can paint a house in 4 hours, and John can paint the same hou [#permalink] New post   02 Nov 2012, 13:17
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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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Re: If Sally can paint a house in 4 hours, and John can paint the same hou [#permalink] New post   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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Re: If Sally can paint a house in 4 hours, and John can paint the same hou [#permalink] New post   02 Nov 2012, 13:30
actleader wrote:
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 the same hou [#permalink] New post   14 Nov 2012, 04:13
\(\frac{1}{4}+\frac{1}{6}=\frac{10}{24}=\frac{5}{12}\)

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

Answer: B
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Re: If Sally can paint a house in 4 hours, and John can paint the same hou [#permalink] New post   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
Answer is A
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Re: If Sally can paint a house in 4 hours, and John can paint the same hou [#permalink] New post   27 Jun 2017, 14:40
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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?

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

Hence, Answer is A
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Re: If Sally can paint a house in 4 hours, and John can paint the same hou [#permalink] New post   23 Sep 2018, 10:41
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.

Hence Answer A


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.
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Re: If Sally can paint a house in 4 hours, and John can paint the same hou [#permalink] New post   17 Dec 2019, 12:43
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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


Output = 1 House to Paint ,Time = 4 Hrs ,
Sally's rate = 1/4
Output = 1 House to Paint ,Time = 4 Hrs,
John's rate = 1/6

Together their Work rates are 1/4+1/6 = 10/24

TArget Question: how long will it take for both of them to paint the house together?

Time = Output/ Joint Rate

= 1 / ( 10/24 )

=12/5 hours or 12/5*60 = 144 minutes

144 Mins =2 Hours and 24 Mins ( A)
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Re: If Sally can paint a house in 4 hours, and John can paint the same hou [#permalink] New post   18 Mar 2021, 05:06
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Solution:

Let the total work be LCM(4,6) = 12 units

Efficiency of Sally = 12/4 = 3 units

Efficiency of John = 12/6 = 2 units

Together, they complete 3+2 = 5 units of work/hr

Hence, total time to complete the work of 12 units working together = 12/5 =2.4

0.4 hours = 4/10 *60 =24 min

Hence 2hrs 24 min. (option a)

Hope this helps :thumbsup:
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Re: If Sally can paint a house in 4 hours, and John can paint the same hou [#permalink] New post   23 Mar 2021, 05:45
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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

Solution:

We see that Sally’s rate is 1/4 and John’s rate is 1/6. Therefore, their combined rate is 1/4 + 1/6 = 10/24. Since time is the inverse of rate, it takes them 1/(10/24) = 24/10 = 2.4 hours, or 2 hours and 24 minutes, to paint the house together.

Answer: A
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Re: If Sally can paint a house in 4 hours, and John can paint the same hou [#permalink] New post   11 May 2023, 14:27
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Re: If Sally can paint a house in 4 hours, and John can paint the same hou [#permalink]
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