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## Algebra (all content)

### Course: Algebra (all content)>Unit 15

Lesson 3: Word problems with multiple units

# Measurement word problem: running laps

Sal solves a US customary distance word problem involving miles, yards, and feet. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• how much is a furlong and what is a furlong • get Grammarly. you can double-click on stuff and it shows the definition when you are in a dock it also shows synonyms that you can use. also, it shows how to correctly type something so you won't have many questions. A unit of length equal to 220 yards, a mile, or 201.168 meters, is now only used in measuring distances in horse racing. according to grammarly
• Why isn't there a video on the eternal question: "How many fluid ounces will fit into X amount of cups?" because, I'm sorry, I can't figure it out. I've taken the time to understand it for HOURS now and I can't figure it out. It gets to the point where I start to ask questions that are irrelevant to the math, always a great sign: "Why do I need to figure how many fluid ounces fit into how many cups? Why is this relevant? When will I EVER need this skill?" I take the time to carefully read the instructions and the question (and of course, the hints afterwards) with - over the years over trying over and over - a figurative team of scientists behind me and I still can't figure this out. Everytime I think I understand the workings of this small exam created by aliens, the answer I give in is wrong, and it's yet again back to the drawing board, over and over and over AND OVER again.

I'm sorry, but this is getting to the point of stupidity. Or it already got to that point. Can somebody, in plain and simple language, explain to me how much cranberry juice Molly needs? Because, judging by the explanation and this entire concept, I seriously don't think she knows. • How many yards are there in a meter? • While I'm clear with most on the material on the exercises for this part of the unit, I've been having a tough time conceptualizing the "wall" questions. You don't exactly solve them using dimensional analysis (at least when I saw how KA solved it. Please correct me if I'm wrong), so it messes with my brain. For example, a question would go as the following:

"It takes 36 minutes for 7 people to paint 4 walls...How many minutes does it take 9 people to paint 7 seven walls?"

So my mind takes some really messy pathways in an attempt to solve the problem, leading to never ending loop of trial and error. Therefore, could anyone breakdown the process of solving the problem so I could understand how it is solved and why you would solve it that way? Thanks. • Each person paints walls with a certain speed measured in `(w)alls/(m)inute`. Let's say it is `xw/ym`. And since there are 7 people, we can assume that the overall speed with which walls are getting painted is 7 times that, or `7xw/ym`, And we know that the overall speed was `4 walls/36 minutes`, or `1w/9m`. Now we can set up an equation: `7xw/ym = 1w/9m`. And to figure our what `xw/yw` equals to, we just need to multiply both parts by 1/7. `7xw/ym * 1/7 = 1w/9m * 1/7` = `xw/ym = 1w/63m`. So it takes 63 minutes for 1 person to paint a wall.

Now that you know the speed, you can set up the second equation: `9 * 1w/63m = 7w/xm` = `9w/63m = 7w/xm` = `1w/7m = 7w/xm` *1/7 = `1w/7m * 1/7 = 7w/xm * 1/7` = `1w/49m = 1w/xm`. So, `x = 49`.
• how do you convert square meters back to meters • What are imperial units? • Definition of Imperial Units :

A system of weights and measures originally developed in England. Similar but not always the same as US standard units.

Examples of Imperial measures :

Length : inches, feet, yards
Area : square feet, acres
Weight : pounds, ounces,
Volume : fluid ounces, gallons

The Imperial System has been replaced by the Metric System in most countries (including England).
• Where did he get 11 from at - when he said 11*300? • D runs circular track in 120 seconds. B running in opposite direction meets d every 48 seconds. S running in same direction as B, passes B every 240 seconds. How often does S meet D? • While this may seem like a complex problem at first glance, you can take a very simple and logical shortcut. First, recognize that the track length is insignificant and has no effect on the problem. Units are also irrelevant, except noting that your final answer will be in seconds. Then find that you can change the speed of D, while having no effect on S and B, since they just change proportionally in response.

Thus, assume the length of the track is 1 and D is stationary. (Their speeds in this special scenario represent their relative speeds in the problem we are actually doing, which can be used to solve for when they meet. From now on, all "speeds" I mention in this scenario will refer to their relative actual speeds). Obviously, that would mean B runs at a speed of 1/48 using distance = rate x time. Then, for S to meet B in 240 seconds, S would have to run an additional 1 length (one more lap of length 1). That means that in 240 seconds, the distance traveled by S, which is the rate (r) times 240, is one more than the distance traveled by B, which is 1/48 times 240, since you already solved the speed of B. You can write this as the equation 240r = 240/48 + 1. Solving for r, we get 1/40 as the speed of S. Since we assumed D to be stationary, the time it takes for S to meet D is just the time it takes for S to make a full lap, or 40 seconds, using d=rt once more.

I hope this helps, if anything is confusing please let me know so I can clarify! :)  