Comparing linear functions word problem: walk

Elizabeth starts out five miles away from school and walks away from school at three miles per hour so she's already five miles away and she's going to walk even further away at three 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 zero 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 zero so we know where they were at time one two and three and so let's think about their rate towards or away from school so and remember this is distance from school so for as we increase as we go from our one to our two Gordon gets two miles closer so his distance to school is decreasing so where was he at time equals zero I'll put time equals zero up here because I don't have these actually I'll put it right here I'll try to squeeze it into the chart so where was he at time equals zero well he would have been two miles further so he would have been six miles away notice it's consistent in the first hour he would have gotten two miles closer to school then the next hour he would have gotten two miles even closer and in the third hour he actually gets two miles closer and he actually gets to school so Gordon started out six miles away at T equals zero so Gordon did start out farther from school than Elizabeth so we can circle Gordon he meets the conditions I was think about Giovanni so at time one he's five miles away from school that at time two or time or at one hour he's five miles away after two hours he's six miles away so he's getting further from school so this is a plus one and then after another hour he's seven miles away so every hour that goes by he's a mile further he's going one mile our away from school so where was he at time equal zero well he would have been a mile closer to school relative to time equal one so he would have been four miles away so he did not start out farther than Elizabeth who started out five miles away now let's look at Hanna Hanna at every time is just fought exactly five miles away from school so she's napping or something she is not actually moving so Hanna didn't she started out a you know napping at exactly the same distance as Elizabeth but she did not start out farther from school than Elizabeth so Hanna does not meet the cry the criteria now let's look at Alberto at time equals one he is nine miles from school and then after one hour he gets a mile and a half he gets a mile and a half further from school after another hour he gets a mile and a half a mile and a half even further so where was he at time equals zero well he would have been a mile and a half closer to school so nine minus 1.5 is he would have been seven and a half miles away so even though he even though he's going away from well he definitely started further from school than Elizabeth Elizabeth started out five miles away Alberto started off seven and a half miles away and it's going even further and further and further so the two students that started out farther from school than Elizabeth are Gordon and Alberto