H> Graphing out Word problems ( Word eq. included)

  • Thread starter Larrytsai
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In summary, Mary and John were running towards the same destination, with Mary starting first at a speed of 7m/s and John starting 35 seconds later at a speed of 8m/s. When John caught up to Mary, they had both traveled the same distance and the time that had passed was 35 seconds. To graph their positions over time, plot Mary's position at the origin and use her slope (7m/s) to draw her line. Then, plot John's position starting at 35 seconds with a slope of 8m/s. This will show their positions at any given time and where they meet on the graph indicates when John catches up to Mary.
  • #1
Larrytsai
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Mary left home at noon running at 7m/s towards school. Her brother John left 35 seconds later running at 8m/s. How much time passed and how far were they from the house when John caught up to Mary.

Can u please state your formula and how to graph it out. I used the x-y graph but when i get to 35seconds with mary its at 245 metres. My problem is how do i graph john on the graph. where do i start? at 0 or 35? please help and thnx alot
 
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  • #2
Plot position (ordinate) vs time (abscissa).

Take time t=0 when Mary leaves the home (origin). What is the slope of her line?

John's position is 0 at t = 35 s. What is the slope of his line?
 
  • #3


To graph this problem, we can use the formula d=rt, where d is the distance, r is the rate (or speed), and t is the time. We can also use the formula d=vt, where v is the initial velocity and t is the time.

First, let's plot Mary's distance on the graph. Since she left home at noon, we can start her at the origin (0,0) and her rate is 7m/s, so her equation would be d=7t. We can plot points on the graph using different values for t. For example, at t=1 second, Mary would be 7 meters away from the origin (1,7). At t=2 seconds, she would be 14 meters away (2,14), and so on. We can continue plotting points until we reach 35 seconds, which is where John starts running.

Next, we can plot John's distance on the same graph. Since he starts running 35 seconds after Mary, his equation would be d=8(t-35). We can plot points on the graph using different values for t, starting at 35 seconds. For example, at t=35 seconds, John would be 0 meters away from the origin (35,0). At t=36 seconds, he would be 8 meters away (36,8), and so on. We can continue plotting points until we reach the point where John catches up to Mary, which is where their distances are equal.

To find the time and distance when John catches up to Mary, we can set their distance equations equal to each other: 7t=8(t-35). Solving for t, we get t=280 seconds. This means that after 280 seconds, John will catch up to Mary.

To find the distance they are from the house when John catches up to Mary, we can plug in t=280 into either equation. Using Mary's equation, we get d=7(280)=1960 meters. This means that after 280 seconds, Mary will be 1960 meters away from the house. Since John catches up to her at this point, he will also be 1960 meters away from the house.

In summary, we can plot Mary's distance on the graph starting at the origin and using the equation d=7t. We can then plot John's distance on the same graph starting at 35 seconds and using the
 

1. How do I graph a word problem with an equation in it?

To graph a word problem with an equation, you first need to identify the relevant variables and assign them to the x and y axes. Then, plot the points from the equation on the graph and connect them to create a line or curve that represents the relationship between the variables.

2. What is the purpose of graphing a word problem with an equation?

The purpose of graphing a word problem with an equation is to visually represent the relationship between the variables in the problem. This can help with understanding the problem, making predictions, and solving for unknown values.

3. How do I know which type of graph to use for a word problem?

The type of graph to use for a word problem depends on the type of relationship between the variables. If the relationship is linear, a line graph should be used. If the relationship is non-linear, a scatter plot or curve graph may be more appropriate.

4. Can I use a calculator to graph word problems?

Yes, most scientific and graphing calculators have the ability to graph equations and word problems. Some even have specific functions for graphing word problems involving multiple variables.

5. Are there any common mistakes to avoid when graphing word problems?

One common mistake when graphing word problems is not labeling the axes and units of measurement. It's important to clearly label the x and y axes and include the units to avoid confusion. Additionally, make sure to correctly plot the points from the equation and accurately connect them to create the graph.

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