Tom, Amanda and Harry working alone can finish a task in 4, 6 and 12hr

Question

Tom, Amanda and Harry working alone can finish a task in 4, 6, and 12 hours respectively. Tom, Amanda and Harry start working together and work for 1 hour, then Tom left and then Amanda and Harry work together for 1 hour, then Amanda left and the rest of the work is done by Harry alone. If the task was started at 10:00 am, then at what time does the task get completed?

(A) 2:30 pm
(B) 3:00 pm
(C) 3:30 pm
(D) 4:00 pm
(E) 4:30 pm

(A) 2:30 pm
(B) 3:00 pm
(C) 3:30 pm
(D) 4:00 pm
(E) 4:30 pm

chetan2u · Accepted Answer

Tom can finish the work in 4 hours, and he works for ONE hour, so he does  \frac{1}{4}^{th}  of the work..
Amanda can finish the work in 6 hours, and she works for first TWO hours, so she does  \frac{2}{6} =\frac{1}{3}^rd  of the work..
Remaining work =  1-\frac{1}{4}-\frac{1}{3}=\frac{5}{12}  is done by Harry..

Harry completes the work in 12 hours, so he will complete  \frac{5}{12}^{th}  of work in  12*\frac{5}{12}=5  hrs
So, the work will finish at 10:00+5hrs=3:00 pm..

B

hiiamgood · Answer

SOLUTION

so take the lcm of 4,6,12 
which is 12 this is work lets assume 
rate=work /time 
so 
tom=(12/4)=3
amanda=(12/6)=2
harry=(12/12)=1

now 
add the rates they said first 1 hour t,a ,h worked together 
3+2+1=6
this is from 10 am to 11 am 
now tom leaves 
so a and h 
its 2+1=3
from 11am to 12 am
so from 10am to 12 am the rate of work done is 6+3=9
now we should know how much left over work is done by harry (so do total work( minus -)the work from 10am to 12 am)
now as we assume the work to be 12 the trick is do 12-9=3(try this with any combination of numbers ull get correct ans )
now the rate harry is 1 and time=work/rate => 3/1
so now its 3 hours from 12 am

and is c 3:00 am

ScottTargetTestPrep · Answer

Solution:

We see that the rates of Tom, Amanda, and Harry are 1/4, ⅙, and 1/12, respectively.

In hour 1, 1/4 + 1/6 + 1/12 = 3/12 + 2/12 + 1/12 = 6/12 = 1/2 of the task has been completed, and thus 1 - 1/2 = 1/2 of the task is left.

In hour 2, 1/6 + 1/12 = 2/12 + 1/12 = 3/12 = 1/4 of the task has been completed, and thus 1/2 - 1/4 = 1/4 of the task is left.

Since Harry is the only person working on the remaining 1/4 of the task, it will take him (1/4)/(1/12) = 1/4 x 12 = 3 hours to complete the remaining 1/4 of the task. Since he started working alone at 12:00 pm, the task will be completed at 3:00 pm.

Answer: B

tbhauer · Answer

In 1 hour:
Tom finishes 1/4 of a task, Amanda 1/6 and Harry 1/12 each hour they work
1st hour: 1/4 + 1/6 +1/12 = 3/12 + 2/12 +1/12 = 6/12 of the task 
2nd hour: 6/12 + 2/12 + 1/12 = 9/12 of the task
3/12 of the task is left, and Harry completes 1/12 each hour, so 3 additional hours are needed for a total of 5 hours
10 AM + 5hrs = 3 pm
Ans = B

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Tom, Amanda and Harry working alone can finish a task in 4, 6 and 12hr

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Tom, Amanda and Harry working alone can finish a task in 4, 6 and 12hr

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