Working alone, Raluca, Ioana and Andreea

Question

Working alone, Raluca, Ioana, and Andreea can complete a job in 6 hours, 4 hours, and 12 hours, respectively. Yesterday, they started the job at 12:00 noon and finished it at 2:30 PM. During that time, each took one break of equal length.

How long was each break?

A. 10 minutes
B. 15 minutes
C. 20 minutes
D. 24 minutes
E. 30 minutes

How long was each break?

A. 10 minutes
B. 15 minutes
C. 20 minutes
D. 24 minutes
E. 30 minutes

ankushsambare · Answer

Let each break be  b hours .
Raluca's rate = 1/6 job per hour
Ioana's rate = 1/4 job per hour
Andreea's rate = 1/12 job per hour
Combined rate:
1/6 + 1/4 + 1/12
= 2/12 + 3/12 + 1/12
= 6/12
= 1/2
So together they complete  1/2 of the job per hour .
They worked from 12:00 PM to 2:30 PM, a total of  2.5 hours .
Since each took a break of b hours, each actually worked:
2.5 − b hours
Total work done:
(1/2)(2.5 − b) = 1
Multiply by 2:
2.5 − b = 2
b = 0.5 hour
= 30 minutes
 Answer:E. 30 minutes .

inciduntveniam · Answer

Shouldn't answer be 10 mins? 30 min is the TOTAL BREAK but the question asks us EACH BREAK? so 30/3 = 10 min break/person

FrozenDragon · Answer

Imagine all three work for 2 hours straight. now their work is finished but still each of them have 30 minutes break left.

I hope this helps

inciduntveniam · Answer

oh right! so silly of me to miss this. thankyou!

Adit_ · Answer

Each took a break of x length.
We could otherwise frame it as, all 3 working together for y mins and the remaining extra time is the break, to make calculation straightforward.
This is because during that break we can say all 3 take a break at the same time. It doesn't matter when they take a break, we can simply assume all 3 take a break at the same time for the same duration.

So,
(R+I+A)*x = 1
On substiuting the rate values for each of the 3:
x = 2hrs.

Remaining  30 mins  this is the break for each of them.

=========================================

Each of them dont take a break for 30/3 = 10 mins because all 3 of them take a break at the same time in our assumption, so all 3 take a break for 30 mins only.

Working alone, Raluca, Ioana and Andreea

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Working alone, Raluca, Ioana and Andreea

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