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

Question

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

BrentGMATPrepNow · Accepted Answer

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:  A

shrinivas280390 · Answer

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

MariaF · Answer

Thanks a lot

I really made a stupid mistake :/

actleader · Answer

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

RJSPO · Answer

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

actleader · Answer

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)?

RJSPO · Answer

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

mbaiseasy · Answer

\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

sasyaharry · Answer

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

ydmuley · Answer

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

HimanshuW11 · Answer

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.

mimajit · Answer

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)

CrackverbalGMAT · Answer

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

Devmitra Sen (GMAT Quant Expert)

ScottTargetTestPrep · Answer

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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