Question

Did I get the correct answer?

Question: You want to make 5880 parts using a machine. Initially, it takes 400 seconds to make 1 part. Each time 60 parts are made, the time is takes to make a part is reduced by 2 seconds. How long (in hours and days) would it take to make the 5880 parts assuming no other time taking factors?

My Answer:

Time it takes to make a part =
400 - 2(x/60), where x = parts made, and is a whole number.

Time it takes to make 5880 parts, assuming no time is saved:
5880 parts X 400 seconds = 2352000 seconds

Answer 1

Time in seconds saved: summation from 1 to 5880, 400-2(x/60)
= 1775662 seconds.

2352000-1775662 = 576338 seconds = 9605.3333 minutes = 160.0938 hours = 6.6705 days

Answer 2

I think it may be wrong, I would think it may take longer

Answer 3

@Destinymasha I did the problem, is this right?

Answer 4

@jim_thompson5910

Answer 5

I'm pretty sure I have it in summation form.

So we want to make 5880 parts. Each time 60 is made, 2 seconds is reduced from making time per part. So 5880 divided by 60 is 98. That is 98 groups of 60 parts, which means 98 reductions of 2 seconds. 2 times 98 is 196 seconds. So, the last group will have each part completed in 400-196 = 204 seconds.

We can write this as:

\[60(400) + 60(398) + ... + 60(204)\]

Factoring out the 60:

\[60(400+398+...+204)\]

You can do the math or write it as a sum:

\[60*\sum_{i=1} ^{98}[400-2*i]\]

Answer 6

That's just my guess but I would look for someone more advanced to confirm.

Answer 7

Wolfram says the above summation = 60(29498) = 1769880

Answer 8

Can you check the back of your book?

Answer 9

Also, i should start at zero in my sum, and this would mean 97 groups of 2-second reductions, not 98, as the 1st group is just 400 seconds per part.

Answer 10

http://www.wolframalpha.com/input/?i=60%28sum+400-2i%2C+i%3D0+to+98%29

Answer 11

And the last group should be 206 seconds per part, not 204.

Answer 12

and the sum should go to 97.. lol

Answer 13

http://www.wolframalpha.com/input/?i=60%28sum+400-2i%2C+i%3D0+to+97%29 :P

Answer 14

I would think you could use calc, but I don't know it

Answer 15

Alright, I think that's it. I would ask someone else to double check it though.

\[60*(\sum_{i=0} ^{97}[400-2i])\]

Answer 16

What does that equal to? The amount of seconds saved or the total time it takes?

Answer 17

Total time. (60 parts * (time per part group 1)) + (60 parts * (time per part group 2)) ... etc all the way to group 98

Answer 18

Or since our i started at zero, we can say from group 0 to group 97, group 0 being 400 seconds per part

Answer 19

that seems to make sense

Answer 20

thanks a lot :)

Answer 21

I kind of thought my answer was right...oh well, it was too small as I thought

Answer 22

I was playing with your sum and I think the only reason it's wrong is because it changes the time per individual unit built rather than per group of 60. 2- i/60 will differ for each i. But it's very close.

Answer 23

I see

Answer 24

You're right

Answer 25

calculate*

Answer 26

...Now (a while later) it says that the machine can only run for 5.5 hours before needing to recharge. It takes 25 minutes for the machine to recharge, how long would it take to make the 5880 parts? :<

Answer 27

So take the total time it took in hours, divide that by 5.5, and you have the number of intervals it could run at. How many breaks are between those times the machine is running? Multiply that number of breaks by 25 minutes, and then add that total amount of time (convert units to hours first) to the number of hours it took running continuously.

Answer 28

The only question is, did you have to charge the machine before you initially started it, or were you able to run it from the go, draining it, and then charging it? Your answer will vary by 25 minutes depending on that.

Answer 29

divide by 5.5.. i didn't do the math, could be a typo, but 5.5, not 5

Answer 30

I'm sure I'm boring you by now

Answer 31

Alright, so that's your number of intervals the machine is running, in hours.

Answer 32

89.981818 repeating

Answer 33

1781640 seconds /60 = 29694 minutes
29694 minutes /60 = 494.9 hours
494.9 hours/5.5 hours = 89.9818, where 18 is repeating

Answer 34

(89.98181818181818-1)*25 = 2224.5454545454545

I'm lost on what that number is. The amount of minuets used during recharge?

Answer 35

Yeah, well, 88.981818...... * 25 because there are N-1 spaces between N objects. For example, let's say it took 10 hours to build everything, and the machine could only run 2 hours at a time. So 10 / 2 = 5 number of times that the machine runs. Now, N = 5, and N-1 = 4 spaces between the times that the machine is running. That is, 4 times you have to charge the machine. If the machine takes 15 minutes to charge, 4 * 15mintes = 1 hour of total charging time. So total run time was 10 hours, + 1 hour charge time = 11 hours total.

Answer 36

In which case, convert them into seconds and add that to the total time in seconds

Answer 37

college

Answer 38

I got 1.91511272727272727 × 10^6 seconds
or 531.975757575757575 hours
or 22.16 days.

I estimated almost a month, I guess I was right.

Answer 39

that's it, you can leave now and never have to help me with this again :)

Answer 40

lol alright good luck with your studies