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Question 220153: Where N is the size of the file in bytes and t is the number of seconds since the download began. in how many minutes will 25 percent of a 500000-byte file remain to be downloaded round to the nearest minute.
Percent remaining= 100 - (42000 divided by N)t
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! The statement of your problem has a flaw, or I may be mis-reading it.
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the formula states:
Percent remaining = 100 - (42000 divided by N)*T
It should state:
Percent Remaining = 100 Percent - (42000 divided by N) * T
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It would then state as follows:
Let R = Percent Remaining
Let N = Number of bytes in the original file.
Let T = Time in Seconds
Let X = Transmission Rate per Second.
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Your formula would then be:
R = 100% - (X/N)*T
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R would equal 25%
X would equal 42000 bytes per second
N would equal 5000000 bytes
T is what we would want to solve for.
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Your formula would become:
25% = 100% - (42000/5000000)*T
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We would subtract 25% from both sides of this equation and we would add (42000/5000000)*T to both sides of this equation to get:
(42000/5000000)*T = 100% - 25% which would become:
.0084*T = 75%
We would then divide each side of the equation by .042 to get:
T = 75%/.0084 = 8928.571429% seconds
In order to get seconds, we would then have to divide by 100% to get:
T = 89.28571429 seconds.
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This is cumbersome and you have to know that you need to divide % seconds by 100% in order to get seconds at the end.
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The formula would have been much better stated as:
.25 = 1 - (42000/5000000)*T
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Then that conversion at the end would not have been necessary.
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Your general formula would then have been:
R = 1 - (X/N)*T
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R would equal Percent Remaining / 100% = 25% / 100% which would equal .25
X would equal 42000 bytes per second
N would equal 5000000 bytes
T is what we would want to solve for and would still be in seconds.
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Your Formula would become:
.25 = 1 - (42000/5000000) * T
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we would solve for T as before.
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T is stated in seconds.
The problem requested minutes.
Divide seconds by 60 seconds per minute to get minutes and your answer becomes:
T = 89.28571429/ 60 = 1.488095238 minutes
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To confirm your answer is correct, you would replace your original equation with known values of T and solve to see if it is true.
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Your original equation is (after my restatement):
25% = 100% - (42000/5000000)*T
We would replace T with 1.488095238 * 60 = 89.28571429
Formula would become:
25% = 100% - (42000/5000000)*89.28571429 which would become:
25% = 100% - .75 which would become:
25% = 100% - 75% after we converted .75 to 75% and would finally become:
25% = 25% confirming the number of seconds for T was correct.
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Again, however, we had the complication of % in the equation which would have been eliminated had we converted Percent to Rate up front.
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Your original equation would then have become:
.25 = 1 - (42000/5000000)*89.28571429
which would then have become:
.25 = 1 - .75 which would then have become:
.25 = .25 directly without any conversion being necessary.
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I haven't seen Percents in equations for some time now. Most of the time they are converted to rates before the equation is solved. This threw me for a little while but I was finally able to figure it out. Hopefully this analysis will help you to understand better as well.
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