10. Bart is writing on a chalkboard that is initially empty. It ordinarily takes Bart 50
minutes to cover the whole board. Nelson is erasing the board while Bart is writing.
Nelson can erase the whole board in 80 minutes by himself. If they work
simultaneously, how long will it be until the whole board is covered?
answer fastly please
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Answer:
Step-by-step explanation:
Bart is writing lines on a chalkboard that is initially empty. It ordinarily takes Bart 50 minutes to cover the whole board; however, today, Nelson is erasing the board while Bart is writing. Nelson can erase the board in 80 minutes by himself. If they work simultaneously, how long will it be until the whole board is covered?
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Bart is writing lines on a chalkboard that is initially : PS Archive
Topic Discussion
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prasannar Apr 25, 2008
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Bart is writing lines on a chalkboard that is initially empty. It ordinarily takes Bart 50 minutes to cover the whole board; however, today, Nelson is erasing the board while Bart is writing. Nelson can erase the board in 80 minutes by himself. If they work simultaneously, how long will it be until the whole board is covered?
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gmatnub Apr 25, 2008
assume the board has 40 lines, nelson can erase .5 lines per minute, and bart can write .8 lines per minute.
.8-.5 = .3 lines/min
40lines x 10min/3lines = 400/3 minutes
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tikpaklong Apr 25, 2008
Bart can do the job (fill the entire board) in 50 minutes, while Nelso can erase the entire board in 80 minutes.
Bart: 1 job / 50 minutes
Nelson: 1 job / 80 minutes
(1 / 50) - (1 / 80) = 3 / 400...
Bart is working at a faster pace than Nelson, so at some point the board will be filled because Nelson can't erase as fast as Bart is writing. Working at the same time, 3 boards will be filled every 400 minutes...which means that 3/400 of the board is filled every 1 minute. The rate that the Board is being filled is 3/400 of the board per minute.
Now, you want the time it'll take to fill one board...this will be the reciprocal: 400/3 minutes.
Conceptually, this is because time = distance / rate...if we think of the distance as the work we need to complete (1 job, or 1 board), and we use the rate of 3/400 board every minute, then we get time = 1 job / 3/400 jobs per minute = 400/3 minutes.
I hope it's help you