Hard QR problems!

[ucla2134]

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Anyone wants to tackle this question.



Tom has to paint his aunt's garage, which will normally take him 10 hours. However, after working half an hour, Tom persuades a friend to paint while he rests. Each half hour later he persuades another friend to join in, and this pattern continues until the job is done: one additional person joins after every half hour, and during each half-hour, only one person is resting. Assuming everyone works at the same rate as Tom, how long will it take until the garage is completely painted?

 

[UCfan]

I did not understand this question thoroughly but as far as I understand I want to say 200 minutes( 3h 20 minutes). Here is my solution
For the first half an hour
1/20 is work done by only Tom
For the second half an hour
1/20 is work done by only Tom's 1. friend
For the third half an hour
2/20 is work done by only two people (one is resting)
For the fourth half an hour
3/20 is work done by only three people (one is resting)
If you realize the pattern this situation can be written as a summation series
Sum(i=0 to n) ai/20=1
The solution gives you 200 min.
If you are not familiar with series
You can do
(1+1+2+3+4+5+x) / 20 = 1
x=4/20
when 7 people are in the group 6/20 can be done (therefore this work is only 2/3 which is equal to 20 min).
30*6+20= 200 min too.
This solution is my understanding. Hopefully it helps.
Sincerely!

 

[ucla2134]

I did not understand this question thoroughly but as far as I understand I want to say 200 minutes( 3h 20 minutes). Here is my solution
For the first half an hour
1/20 is work done by only Tom
For the second half an hour
1/20 is work done by only Tom's 1. friend
For the third half an hour
2/20 is work done by only two people (one is resting)
For the fourth half an hour
3/20 is work done by only three people (one is resting)
If you realize the pattern this situation can be written as a summation series
Sum(i=0 to n) ai/20=1
The solution gives you 200 min.
If you are not familiar with series
You can do
(1+1+2+3+4+5+x) / 20 = 1
x=4/20
when 7 people are in the group 6/20 can be done (therefore this work is only 2/3 which is equal to 20 min).
30*6+20= 200 min too.
This solution is my understanding. Hopefully it helps.
Sincerely!

Thanks so much! Your explanation make much more sense than Kaplan