SOLUTION: Santiago is walking to school, which is straight down the road 500m from his home. He starts out by walking at 2m/s for 2 minutes until he gets to a stop light. He waits 30 seconds

Algebra ->  Graphs -> SOLUTION: Santiago is walking to school, which is straight down the road 500m from his home. He starts out by walking at 2m/s for 2 minutes until he gets to a stop light. He waits 30 seconds      Log On


   

Question 341688: Santiago is walking to school, which is straight down the road 500m from his home. He starts out by walking at 2m/s for 2 minutes until he gets to a stop light. He waits 30 seconds and then realizes that he has left an important essay at the front door, so he runs home at 5m/s. He had forgotten his keys, so he bangs on the door for 3 minutes until his brother Tomas answers. He grabs his essay and runs to school without stopping at 4m/s, arriving just as the warning bell rings.
Provide an equation for each situation and then using appropriate scales, draw thr graph that represents Santiago's journey. Include all equations and time intervals. (7 marks: 1 mark per equation and 2 marks for the graph)
Note: I dont know exactly how the graph looks like, if you could tell me the points, so i can try graphing the points. Thank You!
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

First we will change the speeds from meters per second to meters per
minute.

2 meters per second is 120 meters per minute.
5 meters per second is 300 meters per minute.
4 meters per second is 240 meters per minute.

Here is the graph, where x is the time in minutes, and y is the
distance from home in meters.



He starts at the origin(0min,0m). His goal is to reach the green line which 
is 500 meters. The green line's equation is y=500

He starts out by walking at 120 m/min for 2 minutes. 
So at the end of 2 minutes he has traveled 240 meters.
So we draw a line from (0min,0m) to the point (2min,240m) to indicate the
first part of his trip:



Now we find the equation of the line through (0,0) and (2,240) which is
y=120x%29 for the time interval 0min%3Cx%3C=2min 


 I assume you know how to find the equation of a line
through two points. 

He waits at the stoplight for 30 second (1%2F2 a minute), so
we draw a horizontal line from (2min,240m) to (2.5min,240m), since while
waiting at the stoplight he has not moved any closer to the green
line.



The equation of that horizontal line is 

y=240 for time interval 2min%3Cx%3C=2.5min

Next, he runs home at 5m/s or 300m/min. Now since time=distance%2Frate,
and his distance back home is 240m, that takes him 240%2F300=.8minutes.
so we draw a line from (2.5min,240m) back to the horizontal axis .8 of a minute
later which is 2.5+.8 or 3.3 minutes, to the point (3.3min,0m):

 

So find the equation of the line through (2.5,240) and (3.3,0) which is 
y=-300x+990 for the time interval 2.5%3Cx%3C=3.3

Next he waits 3 minutes at home until his brother answers. so that's
a horizontal line from (3.3min,0m) to (6.3min,0m)

 

The equation of that line is the equation of the x-axis or 
y=0 for the time interval 3.3%3Cx%3C=6.3

Finally he runs the whole 500 m to school without stopping at 
4m/s or 240m/min. We use time=distance%2Frate=500%2F240=2%261%2F12minutes.
So we draw a line from (6.3min,0m) to (6.3min+2%261%2F12min,500m).
To add the minutes 6.3%2B2%261%2F12=6%263%2F10%2B2%261%2F12=6%2618%2F60%2B2%265%2F60=8%2623%2F60min.
So we draw the line from (6.3min,0m) to (8%2623%2F60,500m).

 

The equation of the line through (6.3,0) and (8%2623%2F60,500) is
y= 240x-1512 for the time interval 6.3%3Cx%3C=8%2623%2F60.

If you don't know how to find the equation of a line through 2 points,
then post again asking how.  It amounts to using the slope formula and
the point-slope formula.

So, since he left home the first time, it took him 8%2623%2F60minutes,
or 8 minutes and 23 seconds to get to school. 

Edwin