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CCSS Math: HSF.IF.B.4, HSF.IF.C.9

Elizabeth starts out 5
miles away from school and walks away from school
at 3 miles per hour. So she's already 5 miles away. And she's going to
walk even further away at 3 miles per hour. The table below shows how
far some other students are from school
at various times. Each person is moving at a
constant speed starting at time is equal to 0. Which students started
out farther from school than Elizabeth? Select all that apply. So essentially, we
need to figure out where these students
were at time equals 0. So we know where they
were at time 1, 2, and 3. And so let's think
about their rate towards or away from school. And remember, this is
distance from school. As we increase-- as we
go from hour 1 to hour 2, Gordon gets 2 miles closer. So his distance to
school is decreasing. So where was he
at time equals 0? I'll put time equals 0 up here
because I don't have any-- actually, I'll
put it right here. I'll try to squeeze
it into the chart. So where was he
at time equals 0? Well, he would have
been 2 miles further. So he would have
been 6 miles away. Notice that it's consistent. In the first hour,
he would have gotten 2 miles closer to school. Then the next
hour, he would have gotten 2 miles even closer. And then the third hour, he
actually gets 2 miles closer. And he actually gets to school. So Gordon started out 6
miles away at t equals 0. So Gordon did start out farther
from school than Elizabeth. So we can circle Gordon. He meets the conditions. Now let's think about Giovanni. So at time 1, he's 5
miles away from school. Then at 1 hour,
he's 5 miles away. After 2 hours,
he's 6 miles away. So he's getting
further from school. So this is a plus 1. And then after another
hour, he is 7 miles away. So every hour that goes
by, he's a mile further. He's going 1 mile an
hour away from school. So where was he at time equal 0? Well, he would have been
a mile closer to school relative to time equal 1. So he would have
been 4 miles away. So he did not start out
farther than Elizabeth, who started out 5 miles away. Now let's look at Hannah. Hannah, at every time, is
just exactly 5 miles away from school. So she's napping or something. She is not actually moving. She started out napping at
exactly the same distance as Elizabeth, but she did not
start out farther from school than Elizabeth. So Hannah does not
meet the criteria. Now let's look at Alberto. At time equals 1, he
is 9 miles from school. And then after 1 hour, he
gets a mile and 1/2 further from school. After another hour, he gets
a mile and 1/2 even further. So where was he
at time equals 0? Well, he would have been a
mile and 1/2 closer to school. So 9 minus 1.5 is-- he would
have been 7 and 1/2 miles away. So even though he is
going away from-- well, he definitely started further
from school than Elizabeth. Elizabeth started
out 5 miles away. Alberto started off
7 and 1/2 miles away and is going even further
and further and further. So the two students that
start out farther from school than Elizabeth are
Gordon and Alberto.