ShmoopTube

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Here’s your shmoop du jour…

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Dan and Mike are brothers, and they’re very competitive.

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Sadly, they don’t have a lick of athletic ability, so the only thing they’re really good at is… eating.

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Dan can eat three slices of pizza in four minutes. Mike can eat six slices in ten minutes.

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To the nearest minute, how long does it take the two of them to eat a total of eight slices of pizza?

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Here are the potential answers…

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So… what is this question asking… other than about the root causes of obesity in America?

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This is a rate, time and distance problem and we have to put things in order and figure

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out how they relate with one another.

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Let’s start by creating a little table…

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Dan: 3 slices in 4 minutes

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Mike: six slices in 10 minutes

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To get the total output – or in this case, er… input… the output will come probably tomorrow.

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…we need to calculate the slices per minute that each consumes.

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So… Dan is at three fourths of a slice per minute and Mike is at six tenths of a slice per minute

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which reduces to three fifths of a slice per minute.

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Now we just have to figure out the time it took them to down 8 slices.

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Cleverly, we’ll call that variable… “t.”

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So the equation we get is 3/4 t plus 3/5 t equals 8.

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Now we just need to solve for t and we’re there.

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We need a common denominator – let’s make it 20, easy enough.

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We multiply top and bottom of the first term by 5 to get 15t over 20.

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Then we’ll multiply top and bottom of the second term by 4 to get 12t over 20… then add ‘em together.

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We get 27t over 20 equals 8.

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Now multiply both sides by 20 to get 27t equals 160.

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Divide both sides by 27 and t equals 160 over 27 which is just about 6 minutes.

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…so the answer is A.

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As in, “Abdominal bloating.”

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