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Here’s your shmoop du jour… Dan and Mike are brothers, and they’re very
competitive. Sadly, they don’t have a lick of athletic ability, so the only thing they’re
really good at is… eating.
Dan can eat three slices of pizza in four minutes. Mike can eat six slices in ten minutes.
To the nearest minute, how long does it take the two of them to eat a total of eight slices
of pizza?
Here are the potential answers…
So… what is this question asking… other than about the root causes of obesity in America?
This is a rate, time and distance problem and we have to put things in order and figure
out how they relate with one another.
Let’s start by creating a little table…
Dan: 3 slices in 4 minutes
Mike: six slices in 10 minutes
To get the total output – or in this case, er… input… the output will come probably
tomorrow…
…we need to calculate the slices per minute that each consumes.
So… Dan is at ? of a slice per minute and Mike is at 6 tenths of a slice per minute
which reduces to 3 fifths of a slice per minute.
Now we just have to figure out the time it took them to down 8 slices. Cleverly, we’ll
call that variable… “t.”
So the equation we get is ? t plus 3/5 t equals 8
Now we just need to solve for t and we’re there.
We need a common denominator – let’s make it 20, easy enough.
We multiply top and bottom of the first term by 5 to get 15t over 20. Then we’ll multiply
top and bottom of the second term by 4 to get 12t over 20… then add ‘em together.
We get 27t over 20 equals 8.
Now multiply both sides by 20 to get 27t equals 160.
Divide both sides by 27 and t equals 160 over 27 which is just about 6 minutes.
…so the answer is A.
As in, “Abdominal bloating.”