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International Baccalaureatte | Maths HL
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Date Posted: 3 years ago
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Let x be the number of minutes pipe B takes to fill the tank alone.
Number of minutes pipe A takes to fill the tank alone = x - 40
In 1 minute, pipe B fills 1/x of the pipe (fraction). So in 48 minutes, pipe B fills 48/x of the pipe.
In 1 minute, pipe A fills 1/(x-40) of the pipe.(fraction). So in 48 minutes, pipe A fills 48/(x-40) of the pipe
Since they can fill the tank together in 48 minutes,
48/(x-40) + 48/x = 1
Multiply both sides by x(x-40),
48x + 48(x-40) = x(x-40)
48x + 48x - 1920 = x² - 40x
x² - 40x - 96x + 1920 = 0
x² - 136x + 1920 = 0
(x - 120)(x - 16) = 0
x = 120 or x = 16(rejected, as it would mean x - 40 = -24 , which is negative. Time taken for pipe A to fill the tank alone cannot be negative)
So x = 120, which means Pipe B takes 120 minutes (or 2 hours) to fill the tank alone.
Number of minutes pipe A takes to fill the tank alone = x - 40
In 1 minute, pipe B fills 1/x of the pipe (fraction). So in 48 minutes, pipe B fills 48/x of the pipe.
In 1 minute, pipe A fills 1/(x-40) of the pipe.(fraction). So in 48 minutes, pipe A fills 48/(x-40) of the pipe
Since they can fill the tank together in 48 minutes,
48/(x-40) + 48/x = 1
Multiply both sides by x(x-40),
48x + 48(x-40) = x(x-40)
48x + 48x - 1920 = x² - 40x
x² - 40x - 96x + 1920 = 0
x² - 136x + 1920 = 0
(x - 120)(x - 16) = 0
x = 120 or x = 16(rejected, as it would mean x - 40 = -24 , which is negative. Time taken for pipe A to fill the tank alone cannot be negative)
So x = 120, which means Pipe B takes 120 minutes (or 2 hours) to fill the tank alone.
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