Comparing linear functions
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Charles and Tammy live the same distance from work, and they started walking to work at the same time. They both walked at constant speeds, though not necessarily at the same speed. Charles' distance from work is shown in the following table. So at 50 seconds, he's 830 meters from work. Then another 50 seconds goes by, and now he's 760 meters from work. Another 50 seconds goes by, and he's 690 meters from work, which makes sense. He's getting closer and closer to work as seconds pass by. He's walking to work. Which of these sentences could possibly be true? Select all that apply. So what are these sentences talking about? So it looks like they're all talking about Tammy. Tammy started 830 meters from work and walked towards work at 2 meters per second. She started 900 meters from work and walked towards work at 7/5 meters per second. So all of these seem to be statements about where did Tammy start and how quickly did she walk to work? So let's think about which of these could possibly be true. Well, the one thing that we know is that they live the same distance from work. So the distance that Charles started walking from work, that's the same distance that Tammy started walking from work. So let's figure out what that distance is. So we see that every 50 seconds, so if we go from 50 to 100 seconds, so if we add 50 seconds, or 50 seconds go by, it looks like Charles traveled another-- let's see. To go from 830 to 760, his distance from work decreased by 70 meters. And let's see if that keeps holding up. It should because they're moving at constant speeds. Another 50 seconds goes by, and his distance from work decreases by another 70 meters. So what would have happened 50 seconds in the past? So what would happen at 0 seconds? So 50 seconds before he's at 830 meters, he would have been 70 meters further from work. So he would have been 900 meters from work, and we see that it's consistent. When 50 seconds pass by, when we go from 0 seconds to 50 seconds, he goes from 900 meters away to 70 meters away. So once again, his distance from work decreases by 70. Then another 50 seconds goes by, it decreases by 70 again. Another 50 seconds, it decreases by 70 again. So at time 0, Charles was 900 meters away from work. Now, we know that Tammy and Charles live the same distance away from work. So Tammy would have also started 900 meters away from work. Now, they tell us that they don't necessarily walk at the same speed. So we don't know what Tammy's speed is. This hasn't in any way constrained Tammy's speed. So we know that she started 900 meters away. So we know that this can't be the case. That says 830. We know that this can't be the case. We know that this can't be the case because they all talk about starting at a distance other than 900 meters. And over here, both of these, they say she started at 900 meters from work and walked towards work at 7/5 meters per second. Well, that's possible. It's not necessarily true. They just haven't given us information on her speed. But given the information so far, this is definitely a possibility. Likewise, Tammy started 900 meters from work-- we know that is true-- and walked towards work at 5/7 meters per second. Well, once again, that's a possibility. That hasn't been ruled out by the information right over here. So these two are both possibly true.