Adam, Ben, and Clara are hired to weed a garden at a community center.

Question

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.

AdarshSambare · Answer

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

BongBideshini · Answer

Let rates be:
 
 Adam = A 
 Ben = B 
 Clara = C  
One whole garden = 1 job.
Given:
A + B = 1/6
We need:
Time for A + C
i.e., need the value of:
1/(A + C)

Statement (1): 
A + B + C = 1/4
Since:
A + B = 1/6
C = 1/4 − 1/6
= 1/12
But we still do not know A individually.
 Insufficient

Statement (2): 
Ben takes 50% more time than Adam.
For the same work, the rate is inversely proportional to time.
So Adam’s rate is 1.5 times Ben’s rate.
Therefore:
A : B = 3 : 2
A/(A+B) = 3/5
Given:
A + B = 1/6
A = 1/10
B = 1/15
Still no information about Clara.
 Insufficient

(1) + (2) Combined

C = 1/12
A = 1/10

A + C = 1/10 + 1/12
= 11/60
Time required: 60/11 hours
 Both together sufficient 
 
Answer: C

SS990 · Answer

Answer is C

Given working at the same time, independently, A and B can do 1/6th of the working 1hr. 
To find: how long will A and C take with the same arrangment?

1)All 3 can do the work at the same time, independently, can do 1/4th of the work in 1 hr. so we can find C's work rate this way. But know nothing of A or B or A to find A and C together. so thsi is insufficient

2) B's work realtive to A's work rate is provided. But we know nothing about C's work rate so this is insufficient

Together, We know C's rate from 1st and A's rate from 2nd option, so we can find the answer to the Question at hand.

Hence C

Adam, Ben, and Clara are hired to weed a garden at a community center.

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Adam, Ben, and Clara are hired to weed a garden at a community center.

Prep Toolkit

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