Mary and Jane working together can complete a task in 2 hours and 24

Question

Mary and Jane working together can complete a task in 2 hours and 24 minutes. Jane and Karen working together can complete the same task in 1 hour 20 minutes whereas Karen and Mary working together can complete the task in 1 hour 30 minutes. Which of the following best represents the time taken to complete the task if Mary, Jane and Karen work together?

A. 42 minutes
B. 48 minutes
C. 54 minutes
D. 1 hour
E. 1 hour 6 minutes

A. 42 minutes
B. 48 minutes
C. 54 minutes
D. 1 hour
E. 1 hour 6 minutes

amascarenhas · Answer

Answer E
2h24 min = 144 min =16*9
1h20 min = 80 min = 8*10
1h30 min = 90 min = 9*10

(1/M+1/J)+(1/J+1/K)+(1/K +1/M) =1/144+1/80+1/90
2*(1/M +1/J+1/K)=(10+16+18)/1440 =44/1440
(1/M+1/J+1/K) = 22/1440

1440/22 =65 min...
Working together they will take a little more than 1h and 5 minutes

Answer E

zishu912 · Answer

Mary and Jane together takes 144 minutes
Jane and Karen together takes 80 minutes
Kane and Mary takes together 90 minutes

Let's assume the total unit of work LCM  = 720 units

Hence efficiency of Mary and Jane combined will be = 720/144 = 5 units/min
 efficiency of Jane and Karen will be = 720/80 = 9 units/min
 efficiency of Karen and Mary will be = 720/90 = 8 units/min
Therefore their combined efficiency Mary + jane +Jane+Karen+Karen+Mary = 22------>2(Mary+Karen+Jane) = 22
Mary + Karen+ Jane = 11

So the time taken to complete the work when they are working together = 720/11 = 66 minutes(approx)

Hence E is the correct choice

vikramnugge · Answer

Bunuel  could you help solve this problem.

generis · Answer

Another way: add rates in hours. 
Express time in fractions of hours. 
Rate: invert the time fraction; work rate and time are inversely proportional

M + J 
TIME: 2 hrs 24 mins:   2\frac{24}{60}=2\frac{2}{5}=\frac{12}{5} hours  
RATE:   \frac{5}{12}

J + K 
TIME: 1 hr, 20 mins   1\frac{20}{60}=1\frac{1}{3}=\frac{4}{3} hours  
RATE:   \frac{3}{4}

K + M 
TIME: 1 hour 30 minutes =   \frac{3}{2} hours  
RATE:  \frac{2}{3}

TIME needed for all three to complete the task?

(M + J + J + K + K + M) = (\frac{5}{12}+\frac{3}{4}+\frac{2}{3}) 
 2(M+J+K) = RHS 
 (M+J+K)=\frac{1}{2}*(\frac{5}{12}+\frac{9}{12}+\frac{8}{12})=\frac{22}{24}  
RATE of all three =  \frac{22}{24}

TIME for all three (invert rate)
 \frac{24}{22}=\frac{12}{11}=1\frac{1}{11} hours 
 \frac{1}{11}=.09\approx\frac{1}{10} hour\approx 6 minutes

TIME: 1 hour, approximately 6 minutes

Answer that "best represents" time taken to finish the work if M, K, and J work together?

Answer E) 1 hour, 6 minutes

Mary and Jane working together can complete a task in 2 hours and 24

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