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# Linear functions word problem: fuel

CCSS.Math:

## Video transcript

caryl tilled up the tank of his truck with 400 litres of fuel and set out to deliver a shipment of bananas to Alaska the truck consumed a zero point eight litres of fuel or eight tenths of a liter of fuel for each kilometer driven graph the amount of fuel remaining in the trucks tank in liters as a function of distance driven in kilometers and all right over here we have we have a graph where or we have a coordinate plane where our horizontal coordinate is distance in kilometers and our vertical our vertical axis is fuel and liters so and we can move we can define the line by moving these two points around because two points the final line and so let's just think about two points that we could figure out can we figure out the fuel at two different distances and then that will help us define the line well the first thing that we might want to think about is well what what about before we've traveled at all that might be an easy thing to figure out what was the amount of fuel in the tank when we haven't traveled at all and that they tell us that in in this passage and I encourage you to pause the video and think about that well they tell us Karl filled up the tank of his truck with 400 liters of fuel and then set out to deliver shipment of bananas so before he had driven it all right after he'd filled his tank he had 400 liters of fuel so we could say when distance was zero kilometers he had 400 liters of fuel so we have one point on that line now we've got to think about where we might want to put where we want to put this other point and the way I think about it is well it's just we know he's consuming he's consuming eight tenths of a liter of fuel for each kilometer driven but they don't have you know we're not going by one kilometer two kilometers they're going by this is like 50 kilometers 100 kilometers so let's think about how much fuel he would have consumed after driving 100 kilometers and if he consumed that much we would subtract that from the amount of fuel he started with and then that would tell us that would tell us what at this point would be it's going to be someplace over here and it's going to be it's going to be below 400 because we're consuming fuel fuel should be going down as distance increases this should be a down word sloping line so I have my I have my scratch pad here let me let me get it out and I have the same question there just gives us all the same information but what I want to figure out is so we already know we already know that so we have distance distance let me I'll just write actually let me just write the whole thing to myself a little bit more space distance in kilometers distance in kilometers and then you have fuel you have fuel in liters you have fuel in liters and we already figured out that before he got on right after he filled up his tank but before he set out on his trip at distance 0 kilometers we've already actually plotted that but then we said what what happens at 100 kilometers at 100 kilometers how much fuel will he have well they tell us that he consumes 0.8 liters of fuel for each kilometer so 0.8 liters per kilometer and then we just multiply that times the number of kilometers so times 100 kilometers the units work out kilometers divided by kilometers we're just going to be left with leaders and then we multiply the numbers 8 tenths of 100 well that's going to be equal to 80 and the units are liters 80 liters so at a distance of 100 kilometers he's going to have consumed all right let me be careful here he's going to have consumed 80 liters he's going to have consumed 80 liters so the fuel the fuel is actually going to be what he started with what he started with - how much he consumed so it's going to be minus 0.8 and if we want to write the unit's there I might as well so you know this is liters right over here this is 400 liters and I can write this kilometres kilometres it's going to be 400 litres minus 0.8 litres per kilometer times times we've got clear times 100 times 100 kilometers and same thing kilometers divided by kilometers and we are left with 400 litres minus 0.8 liters times 100 well that's just going to be equal to 400 liters which is how much he started with minus 8 tenths of 100 is 80 and the unit's left is 80 liters so 400 litres minus 80 litres that's going to be 320 liters so when he has traveled 100 kilometers he will have 320 liters left in his tank so let's plot that so when he has traveled 100 kilometers actually I just randomly had put the point there he is going to have 320 liters left in his tank and just like that we have plotted the line that shows how much fuel he has in his tank as a function of as a function of distance travelled and you can even see from this that he's going to run out of fuel at the 500 kilometer mark