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13 May 2026, 19:00
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C
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Adam, Ben, and Clara are hired to weed a garden at a community center. If Adam and Ben, working simultaneously and independently at their respective constant rates, can weed the garden in 6 hours, how long would Adam and Clara, working simultaneously and independently at their respective constant rates, take to weed the garden?
(1) Adam, Ben, and Clara, working simultaneously and independently at their respective constant rates, can weed the garden in 4 hours.
(2) Ben, working alone at his constant rate, would take 50% more time to weed the garden than Adam, working alone at her constant rate, would take.
(1) Adam, Ben, and Clara, working simultaneously and independently at their respective constant rates, can weed the garden in 4 hours.
(2) Ben, working alone at his constant rate, would take 50% more time to weed the garden than Adam, working alone at her constant rate, would take.
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M47-153
09 Jun 2026, 02:15
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GMAT Club Official Solution:
Adam, Ben, and Clara are hired to weed a garden at a community center. If Adam and Ben, working simultaneously and independently at their respective constant rates, can weed the garden in 6 hours, how long would Adam and Clara, working simultaneously and independently at their respective constant rates, take to weed the garden?
Let A, B, and C be the rates of Adam, Ben, and Clara, respectively, in gardens per hour.
We are given that Adam and Ben together can weed the garden in 6 hours, so:
A + B = 1/6
The question asks for the time Adam and Clara would take together, so we need A + C.
(1) Adam, Ben, and Clara together can weed the garden in 4 hours.
So:
A + B + C = 1/4
Since A + B = 1/6:
C = 1/4 - 1/6 = 1/12
But we still do not know A, so we cannot determine A + C.
Not sufficient.
(2) Ben would take 50% more time than Adam to weed the garden.
So Ben’s time is 3/2 of Adam’s time. Since rate is the reciprocal of time, Ben’s rate is 2/3 of Adam’s rate:
B = 2A/3
Since:
A + B = 1/6
we can determine A and B. However, (2) gives no information about Clara’s rate, so we cannot determine A + C.
Not sufficient.
(1)+(2):
From statement (1): C = 1/12
From statement (2): B = 2A/3
Since A + B = 1/6:
A + 2A/3 = 1/6
A = 1/10
Therefore:
A + C = 1/10 + 1/12 = 11/60
So Adam and Clara together would take:
60/11 hours
Sufficient.
Answer: C.
Adam, Ben, and Clara are hired to weed a garden at a community center. If Adam and Ben, working simultaneously and independently at their respective constant rates, can weed the garden in 6 hours, how long would Adam and Clara, working simultaneously and independently at their respective constant rates, take to weed the garden?
Let A, B, and C be the rates of Adam, Ben, and Clara, respectively, in gardens per hour.
We are given that Adam and Ben together can weed the garden in 6 hours, so:
A + B = 1/6
The question asks for the time Adam and Clara would take together, so we need A + C.
(1) Adam, Ben, and Clara together can weed the garden in 4 hours.
So:
A + B + C = 1/4
Since A + B = 1/6:
C = 1/4 - 1/6 = 1/12
But we still do not know A, so we cannot determine A + C.
Not sufficient.
(2) Ben would take 50% more time than Adam to weed the garden.
So Ben’s time is 3/2 of Adam’s time. Since rate is the reciprocal of time, Ben’s rate is 2/3 of Adam’s rate:
B = 2A/3
Since:
A + B = 1/6
we can determine A and B. However, (2) gives no information about Clara’s rate, so we cannot determine A + C.
Not sufficient.
(1)+(2):
From statement (1): C = 1/12
From statement (2): B = 2A/3
Since A + B = 1/6:
A + 2A/3 = 1/6
A = 1/10
Therefore:
A + C = 1/10 + 1/12 = 11/60
So Adam and Clara together would take:
60/11 hours
Sufficient.
Answer: C.
General Discussion
13 May 2026, 19:46
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Let Adam’s rate = A
Ben’s rate = B
Clara’s rate = C
Given:
A + B = 1/6 (garden per hour)
We need A + C.
Statement (1):
A + B + C = 1/4
Since A + B = 1/6,
C = 1/4 − 1/6
= (3 − 2)/12
= 1/12
But we still do not know A.
So we cannot find A + C.
Not sufficient.
Statement (2):
Ben takes 50% more time than Adam.
Suppose Adam alone takes t hours.
Then Ben alone takes 1.5t hours.
Rates:
A = 1/t
B = 1/(1.5t) = 2/(3t)
So,
A + B = 1/t + 2/(3t)
= 5/(3t)
Given this equals 1/6:
5/(3t) = 1/6
5 × 6 = 3t
30 = 3t
t = 10
So,
A = 1/10
B = 1/15
But still no information about C.
Not sufficient.
Combine (1) and (2):
From (1):
C = 1/12
From (2):
A = 1/10
Therefore,
A + C = 1/10 + 1/12
= (6 + 5)/60
= 11/60
Time taken by Adam and Clara together:
1 ÷ (11/60) = 60/11 hours
Unique value obtained.
Answer: C
Ben’s rate = B
Clara’s rate = C
Given:
A + B = 1/6 (garden per hour)
We need A + C.
Statement (1):
A + B + C = 1/4
Since A + B = 1/6,
C = 1/4 − 1/6
= (3 − 2)/12
= 1/12
But we still do not know A.
So we cannot find A + C.
Not sufficient.
Statement (2):
Ben takes 50% more time than Adam.
Suppose Adam alone takes t hours.
Then Ben alone takes 1.5t hours.
Rates:
A = 1/t
B = 1/(1.5t) = 2/(3t)
So,
A + B = 1/t + 2/(3t)
= 5/(3t)
Given this equals 1/6:
5/(3t) = 1/6
5 × 6 = 3t
30 = 3t
t = 10
So,
A = 1/10
B = 1/15
But still no information about C.
Not sufficient.
Combine (1) and (2):
From (1):
C = 1/12
From (2):
A = 1/10
Therefore,
A + C = 1/10 + 1/12
= (6 + 5)/60
= 11/60
Time taken by Adam and Clara together:
1 ÷ (11/60) = 60/11 hours
Unique value obtained.
Answer: C
