3 identical machines each working 8 hours a day, together

Question

3 identical machines each working 8 hours a day, together can complete a task in 10 days. After working together for 2 days, one machine broke. How many hours a day should each of the remaining machines work to complete the task on time?

Please explain your solution.

Hayabusa · Answer

I think it is 12 hours.

3 mach x 8 hrs a day x 10 days finish the job

Total 240 hours

After 2 days - 48/240 of the work is done -->> 192 hours to go

In order to complete on time 2 machines x X hours a day x 8 days =192 hrs

X=12

ggarr · Answer

I get 6 hrs. per machine. 

10 days, 8 hrs per day = 80 hrs to complete a job

the machines work for 2 days and complete 1/5 of the job, 16/80 (16 hrs (2 days)/80 hrs (10 days)) = 1/5
4/5 of the job remains

the rate for all 3 machines is 1/80. the rate for each machine is 1/240 (1/80  /  3 = 1/240)
the combined rate for 2 machines is 1/120 (1/240*2)

final equation:
rt=w
1/120(t)=4/5w, t = 480/5 = 96 total hrs. 96/2 = 48 total hrs. per machine
there are 8 days remaining so 48/8 = 6 hrs. per day per machine

Hayabusa · Answer

If 3 machines have to work 8 hrs per day in order to complete the job and one machine broke, wouldn't they have to work more than 8 hours per day in order to make up ???

KillerSquirrel · Answer

Hayabusa is right.

total task will take 240 hours to finish = 3*8*10 (three machines *eight hours a day*ten days)

since the three machines already worked 2 days they worked for 2*8*3 = 48 hours.

240 - 48 = 192 hours left

since we are left with 2 working machines:

192/2 = 96 hours

and we still have 8 working days:

96/8 = 12

the answer is 12 hours a day !

:-D

Mishari · Answer

3 identical machines each working 8 hours a day, together can complete a task in 10 days. After working together for 2 days, one machine broke. How many hours a day should each of the remaining machines work to complete the task on time? 

3 Machines: X,X, andX
10 days = 80 hours/job for all three machines
OR 1/80 job/hour

1/T = 3/X = 1/80 --> X = 240 hours/ job
For two days  , the three machines completed 16*1/80 = 1/5 of the job.  

2 machines together work at the rate:
1/T = 1/X + 1/X = 2/X = 2/240 = 1/120
T = 120 hours/job OR 1/120 job/hour

Remaining hours to complete the job for two machines working together:

4/5 job x 120 hours/job = 96 hours 

Since only 8 days are left to finish the job  , each of the remaining machine needs to work for 96/8 = 12 hours a day


 ANSWER:   12 hours/day

ggarr · Answer

the end of this prob is confusing me. Hayabusa is right that it makes no sense that the machines are working less time, so 6 is wrong. but isn't 96 hrs being split b/w 2 machines? if so, why isn't it 96/2 = 48 total hrs over 8 days. what the %&*# am I missing?

Mishari · Answer

For my solution, the calculated number of hours left is for each one of the two machines, not for both machines. So no need to split the hours between the two, as long as I've used a combined rate of work. Get it ?

ggarr · Answer

yes, just when I was gonna post the answer to my own question I saw your response. thanks. yes, 96 hrs are split across 2 machines. I failed to divide 48 hrs (the # of hrs it'd take 1 machine to complete the job) by 4 (the # of days that 1 machine would work). I divided 48 by 8, the # of hrs it'd take 1 machine to complete the job by the # of days it'd take both machines to complete the job.

vidyasagar · Answer

M/C----HRS/DAY----TOTAL-DAYS-----WORK-PROPORTION

 3--------8---------------10---------------------100% (1 WORK)

 3--------8----------------2---------------------20% (1/5 WORK).OBIVOUS

 2--------x----------------8---------------------80% (4/5 WORK)

=> 8/x=(2/3)*(8/2)* (20/80)

=> X=12 DAYS

grad_mba · Answer

do we need Math at all for this problem ??

3 - identical machines - work at same rate

so if one machine breaks - the load will equally be shared by other two

8/2 = 4hrs

hence 8 + 4 = 12hrs !

ywilfred · Answer

Each day, the three machine clears 3*8 = 24 hours worth of work.
So over 10 days, there are 240 hours worth of work.

After two days, 48 hours of work is cleared. This leaves 192 hours to be shared among two machines and we want this to be completed within 8 days.

2*x*8 = 192
x = 12 hours.

Caas · Answer

Thank you all for your various solutions. I think grad_mba's way is the easiest

3 identical machines each working 8 hours a day, together

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