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## 7th grade foundations (Eureka Math/EngageNY)

### Course: 7th grade foundations (Eureka Math/EngageNY)>Unit 1

Lesson 3: Topic C: Foundations

# Finding average speed or rate

Using the formula for finding distance we can determine Usian Bolt's average speed, or rate, when he broke the world record in 2009 in the 100m. Watch. Created by Sal Khan.

## Want to join the conversation?

• At , it said Usain Bolt could go 23.3 mph, and I was thinking, considering that Usain is a human, he probably wouldn't be able to keep that pace consistent. Wouldn't it be more accurate to look at how his speed decreased, and then, considering the time it took for him to start decreasing speed, factor that in and figure out how many mph he could? Now, I definitely can't figure out an equation like that, but is there anyone that could?
• Note the title of the video, we're calculating AVERAGE speed. Note that just taking a single 'snapshot' reading could be misleading, as one runner might be faster for a couple seconds, then trip and never make it to the finish!
Back to your point, the bigger variation would be the time to ramp from zero UP to full speed. Being a short race, and he's a world class sprinter, would guess he's still going full tilt at the finish! In a longer race there may be some drop off, but experienced runners know not to wear themselves out with a short initial burst that saps all their energy, and winds up killing their average.
As far as an equation to represent his speed over time, think it would be more a matter of charting the data moment to moment rather than calculating, though I suspect the ramp up from zero to full speed could be approximated with a logarithm.
• I might be confused, but in the significant figures video https://www.khanacademy.org/math/arithmetic/decimals/significant_figures_tutorial/v/multiplying-and-dividing-with-significant-figures Sal tells us that we shouldn't figure out significant figures until you are done with your calculations, but at he shortens the number down to 10.4. Since he continues on to figure out km/s shouldn't he have waited? If he wouldn't have shortened it he would have ended up with 37.6 km/h instead of 37.4, which is a HUGE difference when talking world records.
• That guy was really fast, i don't think you could do that kai.j
• If Usain Bolt's speed was 23.3 miles per hour, then what would be, by rate, his maximum distance in square miles?
• Square miles are not measures of distance, they are measures of area.
• At , Sal says, "We're not changing the fundamental values we're essentially just multiplying it by 1."

The equation at this point is 10.4 m/s times 1/1000 km/m.

Sal then continues by saying the 'm' cancels out. How? They aren't in the same place. If we're multiplying shouldn't the equation be 10.4 times 1/1000 k2m/sm?

Also.... now that I'm looking at it... how did the 1000 get on the bottom?

If we're looking for km/s shouldn't it be 1000/1? This makes the final equation 10.4 m/s times 1000/1 km/s. I don't follow how this makes any sense.
• At about What is dimensional analysis? I don't understand what he meant by that.
• Dimensional analysis is analysis of the units in the equations. The different types of measurements combined into a new one.
• Just a quick point, it can help to remember the SPEED, DISTANCE, and TIME TRIANGLE. In this triangle, you have a D for DISTANCE at the top, a T for TIME in the bottom right corner, and an S for SPEED in the bottom left. Now, put a division symbol between the D and S, and a division symbol between the D and T. Finally, put a multiplication symbol between S and T. Now, the other two points in the triangle make the point you're looking at. For example, S=D/T. So, T=D/S, and D=SxT. Hope this helps! :)
• Can someone please walk me through this STEP BY STEP, regardless of how ridiculously minor the step is? I have tried and failed so many times it's not even funny. I have looked at countless videos, and asked several people for help. I know it is a simple problem, but I am really struggling. Any help would be greatly appreciated.

Two airplanes start at the same time from airports 500 km apart. Each one flies with an airspeed of 200 km/hr directly towards the other airport. But one reaches its airport half an hour before the other plane reaches the other airport. How fast is the wind blowing?

If you can include what laws you use along the way, it would really benefit my understanding. But at the least, i just want to see how to do it. I AM NOT AFTER THE ANSWER. I AM AFTER THE PROCESS. I really just want to understand and I am desperate. Thank you in advance!!
• I'll give it a try.

We have 2 airplanes which need to travel same distance (500km) and both are able to fly at the same speed (200km/h).

Because both plane's travel distance and speed are the same, we only need to calculate time for one of them and it will be the same for the other.

Using Distance = Rate * Time formula we can find out how long it takes for a plane to travel.

Re-arrange the formula to get:
Time = Distance / Rate
Time = 500km / 200km/h
Time = 2.5 hours

Now the problem states one of the planes arrives half an hour before the other. I did 2.5 hours - 0.5 hours = 2 hours. With the wind it takes 2 hours for one of the planes to reach its destination.
It does not say if the second plane's travelling time or speed was changed so I assumed it is unaffected by the wind.

Find out the speed of the plane which was affected by the wind.
I use Distance formula and re-ranged it to find speed (rate):

Rate = Distance / Time
Rate = 500km / 2 hours
Rate = 250km/h
Wind causes the plane to fly at 250km/h

We know that on their own planes are able to travel at 200km/h. Find the difference in speed between a flight without wind (200km/h) and with the wind (250km/h):
250km/h - 200km/h = 50km/h
Thus, wind speed is 50km/h.

I hope somebody knowledgeable will check my work. I'd like to know if I did this right.
• At , it said Usain Bolt could go 23.3 mph, and I was thinking, considering that Usain is a human, he probably wouldn't be able to keep that pace consistent. Wouldn't it be more accurate to look at how his speed decreased, and then, considering the time it took for him to start decreasing speed, factor that in and figure out how many mph he could? Now, I definitely can't figure out an equation like that, but is there anyone that could?