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Question Stats:
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4%
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When Mary paints a house, it takes her 4 hours. When Lisa joins Mary, and they work together, it takes them only 3 hours to paint a house of the same size. How long would it take for Lisa to paint a house of the same size by herself?
A. 5 hr
B. 6 hr
C. 7 hr
D. 12 hr
E. 20 hr
Kudos for a correct solution.
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A. 5 hr
B. 6 hr
C. 7 hr
D. 12 hr
E. 20 hr
Kudos for a correct solution.
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one hour combined work =1/3..
one hour of mary's work=1/4...
so lisa's one hour work=1/3-1/4=1/12..
so total time =12 hrs
ans D
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one hour of mary's work=1/4...
so lisa's one hour work=1/3-1/4=1/12..
so total time =12 hrs
ans D
_________________
Mary = 1/4 house per hour
L+M = 1/3 house per hour
--> L + 1/4 = 1/3
L = 1/3 - 1/4
L = 1/12 house per hour
--> 12 hours to build the house on her own.
Answer D
L+M = 1/3 house per hour
--> L + 1/4 = 1/3
L = 1/3 - 1/4
L = 1/12 house per hour
--> 12 hours to build the house on her own.
Answer D
Posts: 50
Answer is D as guys have written ,but lets consider this little different approach ...
we have general relation for work , time and rate : w= r *t
lets consider the rate of Mary =4 and as we don't have the rate of Lisa , lets name it L ....
so we have : M=4 , L is not Known , total time for those two ladies 3 hours and w= 1 (as the whole task has been done)
lets plug-in these amounts to the relation : (1/4+ 1/L ) * 3 = 1 after a little trimming the relation we have : 3(L+4/4L)= 1 and lets multiple both sides to 4L
so we have : 3* (L+4)= 4L*1 Or : 3L +12 =4L Or : L= 12 , gives us directly the rate of Lisa's work ,so answer is :D
we have general relation for work , time and rate : w= r *t
lets consider the rate of Mary =4 and as we don't have the rate of Lisa , lets name it L ....
so we have : M=4 , L is not Known , total time for those two ladies 3 hours and w= 1 (as the whole task has been done)
lets plug-in these amounts to the relation : (1/4+ 1/L ) * 3 = 1 after a little trimming the relation we have : 3(L+4/4L)= 1 and lets multiple both sides to 4L
so we have : 3* (L+4)= 4L*1 Or : 3L +12 =4L Or : L= 12 , gives us directly the rate of Lisa's work ,so answer is :D
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Answer = D = 12
Let time taken by Lisa = x
Setting up the equation (Rate * time = Work Done)
\((\frac{1}{4} + \frac{1}{x})*3 = 1\)
x = 12
Let time taken by Lisa = x
Setting up the equation (Rate * time = Work Done)
\((\frac{1}{4} + \frac{1}{x})*3 = 1\)
x = 12
EMPOWERgmatRichC
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Expert reply
Hi All,
This question is an example of a "Work Formula" question with a minor "twist" - we have to work backwards to find the rate of one person....
Any time there are two "entities" working on a task together without any major "twists" (e.g. someone stops working or changes the speed with which they work), then you can use the Work Formula to get to the correct answer:
Work = (A)(B)/(A+B) where A and B are the respective rates of the two entities.
We're told that Mary can paint a house in 4 hours and that Mary & Lisa can paint a house in 3 hours. Using this data, we can use the Work Formula:
(4)(B)/(4+B) = 3
4B = 12 + 3B
B = 12
Thus, Lisa takes 12 hours to paint the house on her own.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
This question is an example of a "Work Formula" question with a minor "twist" - we have to work backwards to find the rate of one person....
Any time there are two "entities" working on a task together without any major "twists" (e.g. someone stops working or changes the speed with which they work), then you can use the Work Formula to get to the correct answer:
Work = (A)(B)/(A+B) where A and B are the respective rates of the two entities.
We're told that Mary can paint a house in 4 hours and that Mary & Lisa can paint a house in 3 hours. Using this data, we can use the Work Formula:
(4)(B)/(4+B) = 3
4B = 12 + 3B
B = 12
Thus, Lisa takes 12 hours to paint the house on her own.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
Posts: 1,776
Bunuel
Work done by Mary = 1/4
Work done by Mary and Lisa = 1/3
So work done by Lisa alone = 1/3 - 14
= 1/12
Hence Lisa would take 12 hours.
Hence option D.
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Bunuel
MAGOOSH OFFICIAL SOLUTION:
Here, the rate equation becomes:
(# of houses) = (painting rate) x (time)
When Mary paints a house, it takes her 4 hours. Thus
(1 house) = (Mary’s rate) x (4 hr)
so her rate is 1/4.
When Mary & Lisa paint together, it takes 3 hrs. Thus
(1 house) = (combined rate) x (3 hr)
and the combined rate = 1/3.
To find a combined rate, we add individual rates.
(combined rate) = (Mary’s rate) + (Lisa’s rate)
1/3 = 1/4 + (Lisa’s rate)
(Lisa’s rate) = 1/3 - 1/4 = 1/3*4/4 - 1/4*3/3 = 4/12 - 3/12 = 1/12.
Lisa’s rate is 1/12 of a house every hour, or in other words, 1 house in 12 hrs. Thus, it would take her 12 hours to paint a house of the same size.
Answer: D.
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Expert reply
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Bunuel
Mary’s rate is 1/4, and Lisa’s rate is 1/L. We can create the equation:
1/4 + 1/L = 1/3
Multiplying by 12L, we have:
3L + 12 = 4L
12 = L
Answer: D
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Bunuel
Let the total work be 12 units
Thus, Efficiency of Mary is 3 units/hr & Efficiency of Lisa & Mary is 4 Units/ Hr, hence efficiency of Lisa is 1 unit/hr
Thus, time required by Lisa to paint the house will be 12 Hours, Answer must be (D)
_________________
Posts: 7
Let the total work be 12 unit
Work done by marry in 1 hr = 3unit
Work done by marry and Lisa in one hr= 4 unit
So work done by Lisa in one hr =1 unit
Total time taken by Lisa to complete 12 unit = 12 hr
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Work done by marry in 1 hr = 3unit
Work done by marry and Lisa in one hr= 4 unit
So work done by Lisa in one hr =1 unit
Total time taken by Lisa to complete 12 unit = 12 hr
Posted from my mobile device
Posts: 22
Bunuel
Total Work Let = 12 units
Work rate by Mary = 12/4 = 3 units/hr
Work rate when Both work together = 12/3 = 3 units/hr
We know that rates can be added
Rate of work done by Lisa = 4 - 3 = 1 unit/hr
Time taken by lisa = 12 hrs
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