Hard Work Problem

[rtaha2412]

Thanks for the help. I am stumped on this.

If 6 machines run at the same constant rate, they can complete a job in 8 hours. If only 5 of these machines run at this rate, how many more minutes will be required to complete the same job?

a 38
b 72
c 80
d 90
e 96

[nadcreutz]

Hey,

I believe the correct answer is c=80

It takes 6 machines 480min (8hrs*60min*6machines) to complete the job, which is 80 minutes per machine. Divide 480 by 5 machines, so it takes 5 machines 96 minutes per machine to complete the same job. That is 16 minutes per machine longer, so multiply this difference by 5 and you get 80 minutes.

[goyalsau]

Hey,

I believe the correct answer is c=80

It takes 6 machines 480min (8hrs*60min*6machines) to complete the job, which is 80 minutes per machine. Divide 480 by 5 machines, so it takes 5 machines 96 minutes per machine to complete the same job. That is 16 minutes per machine longer, so multiply this difference by 5 and you get 80 minutes.

I thought all the 6 machines are working for 8 hours simultaneously

I am getting the answer as 96

What is the OA?

[diebeatsthegmat]

Hey,

I believe the correct answer is c=80

It takes 6 machines 480min (8hrs*60min*6machines) to complete the job, which is 80 minutes per machine. Divide 480 by 5 machines, so it takes 5 machines 96 minutes per machine to complete the same job. That is 16 minutes per machine longer, so multiply this difference by 5 and you get 80 minutes.

I thought all the 6 machines are working for 8 hours simultaneously

I am getting the answer as 96

What is the OA?

yeah you right, the answer must be 96...
6 machines work 480 minutes to finish the job ( at constant speed) so each machine works 80 minutes,
1 machine left thus only 5 machines work, they will have to do the job of the left machine thus 80/5=16
so each machine work more than 16 minutes ,,,,

[GMATGuruNY]

Thanks for the help. I am stumped on this.

If 6 machines run at the same constant rate, they can complete a job in 8 hours. If only 5 of these machines run at this rate, how many more minutes will be required to complete the same job?

a 38
b 72
c 80
d 90
e 96

An easy approach is to plug in a value for the work being completed by each machine.

Plug in that each machine completes 1 unit/hour.
Rate for 6 machines = 6*1 = 6 units/hour.
In 8 hours, r*t = 6*8 = 48 units are completed. This is the value of the job.
Rate for 5 machines = 5*1 = 5 units/hour.
Time for 5 machines = w/r = 48/5 = 9.6 hours
Additional time needed = 9.6 - 8 = 1.6 hours = 96 minutes.

The correct answer is E.

[sbeagol1000]

I got E.

1 job/8 hours/6 machines = 1/48 or 48 hours

For 5 machines to do the same job requires 48hours/5machines = 9.6hrs

9.6hrs - 8 hrs = 1.6hrs

1.6hrs(60min) = 96 min

[killerdrummer]

its E option 96 minutes

let us assume rate /day for each machine as r

Six machines for 8 days = 6r x 8 = 48r

now when same work i.e 48r has to be done with 5 machines it will be 48r/5r = 9.6 hours = (8 + 1.6) hours

1.6 hours equals 96 minutes.

I Hope it was clear!

---
KD

[rairavig]

assume total work to be done = 8 units
done by 6 machines in 8 hours
each machine has contibutued in 8 hours = 8 units / 6
= 1.33 Units

5 machines will do in 8 hours 1.33 x 5 = 6.65 units .... (1)
total work is 8 units so teh work left to be done = 8 - 6.65 = 1.35 units .....(2)

from (1)..
1 hours efficiency of 5 machines = 6.65 / 8
= 0.831

number of hours taken to finish left 1.35 units work by 5 machines = 1.35 / 0.831
= 1.6 Hours = 96 Minutes