In a school experiment, students timed each other as they went various

Question

In a school experiment, students timed each other as they went various distances using various gaits, or ways of moving on foot. The table shows their average speeds using each gait to go 5 meters and 10 meters. The students' assumption is that, for each gait, there is a perfectly linear relationship between distance and average speed (i.e., the relationship can be accurately represented by data points on a straight line) for distances between 3 meters and 15 meters, respectively.

Gait  
  Distance
(meters)  
  Average speed
(meters per second)  
 
  Hopping 
 5 
 2.0 
 
  Hopping 
 10 
 3.1 
 
  Speed walking 
 5 
 2.4 
 
  Speed walking 
 10 
 2.6 
 
  Walking backwarc 
 5 
 1.2 
 
  Walking backwarc 
 10 
 1.6 
 
  Walking forward 
 5 
 1.6 
 
  Walking forward 
 10 
 1.8

For each of the following predictions, select  Yes  if, given the students' assumption, the data in the table provide sufficient support for the prediction. Otherwise, select  No .

Bisleri · Accepted Answer

it took me 6 minutes to answer correctly, Data Insights is bringing down my hope

bb · Answer

You guys are making this way too complicated. The instructions were pretty clear that you need lines and you can solve this question in probably 2 minutes (or less if you are a faster grapher than I am). This is not a PS question - this is Data Insights. You have to use data tools and analysis.

INSTRUCTIONS:
(the relationship can be accurately represented by data points on a straight line) for distances between 3 meters and 15 meters

The Question is telling you can expect a linear relationship but you can GRAPH the information too! If you put it on a graph, you can answer it fairly easily, though i made a mistake of not following a good enough scale and doing it quick and dirty and paid for that with time. Anyway, here is a computer drawing of how this question looks like:

However, do not rush even with the chart, write down the intermediary step (whatever you find) before you formulate the Yes/No answer.

Y	N
	X	The average speed for hopping 3 meters would be greater than that for speed walking 3 meters. From the chart we can see that the speed for hopping 3 is 1.5 and the speed walking 3 is 2.1. The answer is NO.
	X	The average speed for speed walking 15 meters would be greater than that for hopping 15 meters. From the chart we can see that speed walk 15 is almost 3. Hopping 15 is 4. The answer is NO.
X		The average speed for walking backward 15 meters would be greater than that for walking forward 3 meters. From the chart we can see that Walking Back 15 is 2 and Walking Forward 3 is 1.5. The answer is YES.

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Bunuel · Answer

In a school experiment, students timed each other as they went various distances using various gaits, or ways of moving on foot. The table shows their average speeds using each gait to go 5 meters and 10 meters. The students' assumption is that, for each gait, there is a perfectly linear relationship between distance and average speed (i.e., the relationship can be accurately represented by data points on a straight line) for distances between 3 meters and 15 meters, respectively.

Gait	Distance (meters)	Average speed (meters per second)
Hopping	5	2.0
Hopping	10	3.1
Speed walking	5	2.4
Speed walking	10	2.6
Walking backwarc	5	1.2
Walking backwarc	10	1.6
Walking forward	5	1.6
Walking forward	10	1.8

For each of the following predictions, select Yes if, given the students' assumption, the data in the table provide sufficient support for the prediction. Otherwise, select No.

You don't need to graph anything or perform exact calculations. Let's simply analyze the speed increases between 5 and 10 meters:

Hopping: ≈ 50% increase
Speed walking: ≈ 10% increase
Walking backward: ≈ 30% increase
Walking forward: ≈ 10% increase

Now, let's evaluate the options:

The average speed for hopping 3 meters would be greater than that for speed walking 3 meters.

The hopping speed for 5 meters is 2 meters per second, while the speed walking speed for 5 meters is 2.4 meters per second. Since the increase in hopping speed from 5 to 10 meters is greater than the increase in speed walking speed, it suggests that the hopping speed grows more rapidly over distance. Thus, the speed for hopping over 3 meters will decrease by a greater factor from 2 meters per second than the speed for speed walking will decrease from 2.4 meters per second.

Answer - NO.

The average speed for speed walking 15 meters would be greater than that for hopping 15 meters.

The speed for speed walking over 10 meters is 2.6 meters per second, while the speed for hopping over 10 meters is higher at 3.1 meters per second. Since hopping speed increases more rapidly with distance than speed walking, the speed for hopping over 15 meters will grow by a greater factor from 3.1 meters per second than the speed for speed walking will from 2.6 meters per second.

Answer - NO.

The average speed for walking backward 15 meters would be greater than that for walking forward 3 meters.

The speed for walking backward over 10 meters is 1.6 meters per second, while the speed for walking forward over 5 meters is also 1.6 meters per second. Both speeds increase over larger distances. Thus, the average speed for walking backward over 15 meters will increase from 1.6 meters per second, while the average speed for walking forward over 3 meters will decrease from 1.6 meters per second.

Answer - YES.

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sayan640 · Answer

Though the most wonderful explanation has already been given by my friend  EDDIE98  ,
I would like to put forward mine as well.
Basically the distance is proportional to the average speed.
So if the average speed is 2m/s for 5 meters and 3.1 m/s for 10 meters , the average speed will be 4.2 m/s for 15 meters because the speed is increasing in equal proportion i.e (3.1 - 2) = .9 m/s
Please find the diagram attached.
For calculating speed for 3 meter distance, simply put it in the equation and solve.
It will be = .2 m/s
Hope the diagrams helped.

Oppenheimer1945 · Answer

Concept of Regression or Linear Relationship.
1) Hop(3)=2-2.2/5=2-0.44=1.5 approx
 SpeedWalk(3)=5-0.4/5 (greater than above)... hence FALSE

2)SpeedWalk(15)=2.6+0.2, Hop(15)=3.1+1.1=4.2 ...hence FALSE

3) SpeedBack(15)=1.6+0.4=2, ForwardWalk(3)=1.6-zzz , the former is greater (no need to calculate the later)...hence TRUE

KarishmaB · Answer

Responding to a pm: The question is based on the concept of slope of a line. It is explained here: https://anaprep.com/geometry-using-slop ... fectively/ Assumption to be taken to be true: For each gait, there is a straight line relation between distance and average speed for distances between 3 meters and 15 meters. So if we plot distance on x axis and speed on y axis, from x = 3 to x = 15 the points will form a straight line. So for every increase of 1 unit in x, y will change by a fixed amount m in the range 3 to 15. Let's look at the predictions. The average speed for hopping 3 meters would be greater than that for speed walking 3 meters. For Hopping, as distance increases from 5 to 10 (an increase of 5 units) the speed increases from 2 to 3.1, an increase of about 1 unit. So speed increases by about 0.2 for every 1 unit increase in distance. Then when distance is 3, speed would be about 1.6 and that is how it would have come up to 2 when distance became 5. For Speed Walking, as distance increases from 5 to 10 (an increase of 5 units) the speed increases from 2.4 to 2.6, an increase of 0.2 unit. So when distance is 3, speed would be about 2.3 Hence, speed walking speed at 3 meters is higher. Select No The average speed for speed walking 15 meters would be greater than that for hopping 15 meters. For Hopping as distance increases by 5 meters, speed increases by 1.1 units. At 15, speed would be 1.1 more than speed at 10 meters so it would be 3.1 + 1.1 = 4.2 For Speed Walking as distance increases by 5 meters, speed increases by 0.2 units. At 15, speed would be 0.2 more than speed at 10 meters so it would be 2.6 + 0.2 = 2.8 Hence, Hopping speed at 15 meters is higher. Select No The average speed for walking backward 15 meters would be greater than that for walking forward 3 meters. Similarly, speed for walking back at distance 15 will be 2. while speed of walking forward at distance 3 will be about 1.5. Hence, speed for walking backward 15 meters would be greater than that for walking forward 3 meters. Select Yes

keshubhturakhia · Answer

A "linear relationship" is one where the for increase of 1 in x-coordinate there is a fixed change 'a' in the y-coordinate. Since in our data as distance increases the speed increases, we have a 'positively' linear relationship.

So by calculating the difference in speed between 5m and 10m for each gait and dividing it by 5, we can find the increase/decrease in speed for that gait, for a respective 1m increase/decrease in distance for that gait.

By using this method we can find the right answers for all questions.

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