QR question

[299678]

---

Members don't see this ad.

Acme aerospace must build its X16 rocket in 120 days. With 75% of this time gone, 420 workers have completed only 3/5 of the project. By what percent must the number of workers increase for the rocket to be completed on time?

Here is the way of my calculation:

total units of work = 120 days x 420 = 50400 units of work

90 days (75% of 120days) with 420 completed 3/5, so

Let's put x = # of additional workers need

30 days x (420 + x) = 20160 units of work (2/5 x 50400)
x = 252

so (252/420)x100 = 60%

But the correct answer is 100%

Could you be able to correct the way of my calculation if you think I am wrong?

 

[Moabmad]

This would be my method but there might be an easier way.

I thought of this as a simple distance = rate * time question.

Where:
Distance = Total Percent Completed
Rate = Production Rate (% completed each day)
Time = Days

Therefore
3/5 = 60 % complete = Production Rate * 90 days (.75*120)
Solve for Production Rate = 60% / 90 Days = 0.667 % complete / Day

Also, we want to know what the new production rate needs to be in order to complete 2/5 of the project in the remaining 30 days.

Therefore Production Rate = 40% / 30 Days = 1.333 % complete / Day

The percent difference yeilds: ((1.333-0.667)/0.667)*100 = 100%

The production rate is dependant on the number of workers and how many hours they work per day. In order to increase the rate by 100% you would need to either increase the number of workers or the working hours by 100%.

The actual number of workers is irrelevent to solving the question and I believe is provided as a distraction.

Hope this helps.

 

[AmpedUp]

Here's a method based on logic/common sense (without setting up any standard equations or anything):

1/4th of 120 days is 30 days (left remaining)

420 Workers have completed 3/5ths of the project. They did that all in 90 days. Therefore, you can think of the project split up in 5 phases with 3 phases already completed. Each phase took 30 days (90/3 = 30)

Now we have 30 days remaining and 2 phases remaining. With 420 workers, that'll take 60 days. Therefore, in order to finish the project in 30 days, we need to double the number of workers, which (on percentage) is adding 100% more workers to the project.

 

[299678]

wow you make this problem in a way more logical and fast. Thank you. However, I still don't understand what's wrong with my calculation. Could you be able to fix my calculation on your logic?

Your explannation was fantastic.

 

[hausee]

You assume total # of work is 420*120, which is not true according to the Qs. Total # of work should be 420*[(120*.75)/0.6], here time should be [(120*.75)/0.6]=150 days if those 420 ppl keep their current rate of production.

I made the same mistake by the way 🙁

wow you make this problem in a way more logical and fast. Thank you. However, I still don't understand what's wrong with my calculation. Could you be able to fix my calculation on your logic?

Your explannation was fantastic.

 

[orthosm2021]

you can also do 2/3*3 = 2. double up.
doing 2/3 of the work in 3X the original speed.

 

[Streetwolf]

They need to do 2/3 the work they've already done (they need 2/5 and they've done 3/5 so that's 2/3 of the completed work).

They need to do it in 1/3 the time (used 75% of the time and only have the other 25%).

So they need to do 2/3 work in 1/3 time. Thus they need to double up on their speed, or raise it by 100%.

 

[hausee]

Cool😎

They need to do 2/3 the work they've already done (they need 2/5 and they've done 3/5 so that's 2/3 of the completed work).

They need to do it in 1/3 the time (used 75% of the time and only have the other 25%).

So they need to do 2/3 work in 1/3 time. Thus they need to double up on their speed, or raise it by 100%.

 

[299678]

Great ! +1