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Linear equations word problems: volcano

CCSS.Math:

Video transcript

Zain is a dangerous fellow who likes to go rock climbing inside an active volcano he is a dangerous fellow he just heard some rumbling so he's decided to climb out as quickly as he can Zane's elevation relative to the edge of the inside of the volcano in meters II as a function of time in seconds is shown in the table below Zane climbs at a constant rate so this guy I mean if we were to draw a volcano here I mean this guy is just kind of you know he's kind of silly so this is this is my my volcano and he is actually climbing on the inside he's climbing on the inside of an active volcano so there's probably you know there's probably smoke and ash and all the other stuff coming out of this thing so this really is this really is dangerous for him and let's say that this right over here is Zane maybe and he's climbing up he's climbing up from inside the active volcano so let's think of what what let's think about what they're telling us so based on the table which of these statements is true so I'm not going to even look at the statements here I'm just going to try to interpret this so at time equals so it is so his elevation as a function of time in seconds is shown in the table below so this elevation is negative 24 when time is equal to zero and this table is done in a kind of a non-traditional way normally we would have the input into the function on the left hand side and then we would have the we would have the function of it on the right hand side and actually I like looking at things that way so I'm going to make it like that so let me let me copy and paste this so I can put on the other side so let me cut and let me paste it paste it right over here so this one now I can think of it a little bit clearer so at time zero he's going to be at negative 24 meters at time 4 seconds he's going to be at negative 21 meters so this makes it a little bit clearer at least in my head at least in my head so let's think about what's happening so where does he start at time equals zero where is he well time equals zero he's 24 meters below the edge of the volcano so this distance at time equals zero this distance right over here is 24 meters and we could even plot this in a graph so let's say so this is his this is his elevation relative to the edge and it is a function of time I'll write it like that and it is negative most of this time so I'm going to make the x-axis a little or I should say the T axis a little bit higher so look something something like that that's our T axis and when T is equal to zero we see that his elevation is negative 24 meters so his elevation is negative 24 meters so he's going to this is right here at 0 seconds and then when time increases by 4 so our change in time is equal to 4 what's his change in elevation well his change in elevation is let's see he's going from negative 24 to negative 21 he increased by 3 so his change in elevation is equal to positive 3 he increased by 3 so at what rate is he increasing his elevation with respect to time well change in elevation is equal to 3 per unit so when his and that's 3 when his change in time when his change in time and remember this triangle just means just the Greek letter Delta shorthand for change in so change in elevation over change in time is 3 over 4 so one way to think about this is that he goes 3/4 of a meter per second 3/4 meter per second the unit's up here is meter the unit's down here is second so he goes 3/4 of a meter per second and we can verify that the next the next little cop the next row here we see our change in time is 8 change in time is 8 so it's twice as much time as past so he should have gone twice as much distance if his rate is constant let's verify that that's the case so he went from negative 21 to negative 15 has changed he is in elevation increased by 6 so change in elevation over change in time is 6 8 which is the same thing as 3/4 so you see that he has this constant change so let's plot a few of these points so when time is 0 is elevation is negative 24 when time is 4 when time is 4 right over there his elevation is negative 21 let's say this it looks something like this negative 21 and so his his elevation as a function of time is going to look something like this it's going to look something like this and I haven't let me actually draw a little bit more to scale because we built one thing that we the other thing that we do know is that when time is 32 his elevation is 0 so let me put that right over there when time is 32 his elevation is 0 so his elevation is a function of time looks something like this something like this and we can plot other points there when time is 4 so 4 is going to be this 1/2 that's 1/4 so 4 is going to be right over there his elevation is negative 21 so this is a general idea he starts at negative 24 meters and he increases at a rate of 340 meters per second so what did these troy which of these choices is correct Zane was 24 meters below the edge of the volcano when he decided to leave and he climbs 3 meters every 4 seconds on the way out that seems right he climbs 3 meters every 4 seconds so we're going to go with that one let's make sure that these aren't right Zane was 24 meters below the volcano when he decided to leave and he climbs 4 meters every 3 seconds no no it's 3 meters every 4 seconds so that's not right zyne was 32 meters below the edge of the volcano no that's not right Zane was 32 meters that's not right either