Converting US Customary units word problems
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On Judy's way home from school yesterday, she ran for half the distance. Then she skipped for 1/4 of the remaining distance and walked the rest of the way home. She walked for a total 360 feet. What is the distance between school and Judy's home? And they say write the answer in the yards. So this is a little tricky right over here. They say, 360 feet, write the answer in yards. And we have to remind ourselves that one yard is equal to 3 feet. So just so we make sure we don't make that careless mistake, let's put all of our information in yards right now. So 360 feet is how many yards? Well there's 3 feet per yard. So we're just going to divide 360 feet by 3. And so 360 divided by 3 is 120 yards. And now we can do the whole problem in terms of yards. So let's think about it. So let me say that this is her entire distance. This is on her way home from school. And then let me draw a line that shows the distance all the way home. So I want to draw this as large as possible, so we have room to write inside of it. So that's school. And that is home. And they first tells us that she ran for half the distance. So let's split this in two. Let's split that in two. And so she ran for half the distance. This is the distance that she ran. It's half the total distance. Then they say, then she skipped for one fourth of the remaining distance. So let's be clear, the remaining distance is what I haven't filled in orange yet. So let's mark that off into fourths of the remaining distance. So that is half the remaining distance. That's just 1/4, 2/4, 3/4. So we took the remaining distance and we divided it into fourths. And they say, then she skipped for 1/4 of the remaining distance. So this is the remaining distance after running. She skipped for 1/4 of it. And then she walked the rest of the way home. So she walked to the rest of the way home, this is the distance that she walked. And this distance right over here is 120 yards. What is the distance between school and Judy's home? So there's a bunch of ways that you could think about this. When we talked about the remaining distance after running, so this was the remaining distance after she ran, after this orange part right over here. You see that this blue section is 3/4 of that remaining distance. 120 yards is 3/4 of this remaining distance. So this is equal to 3/4 of the remaining distance. So how much is 1/4 of each of those remaining distance? Well since this is 3/4, 1/4 is going to be 1/3 of this. 1/3 of 120 is 40. So this distance right over here is 40. This is 40. This is 40. Notice 40 plus 40 plus 40 is 120. And this right over here is also going to be 40. These are all in terms of yards. So the remaining distance is going to be 40 times 4 or 160 yards. So this is 160 yards. Now, what is the total distance? Well this 160 yards, the remaining distance after she ran, that's half of the total distance. So this is 160 yards, then this is going to be 160 yards as well. So 160 yards plus 160 yards? Gives us a total distance from school to home of 320 yards.