The steps involved in the solution of this problem were:
1. First I had to draw a diagram of the problem based on the explanation:
a) Draw a line segment AB.
b) Split the segment into 3 (for part A of the problem).
c) Label the position of the man.
d) Draw another line segment connecting to the one in mentioned in part a (BC) and Label it Train.
2. Next I had to label all the parts of the problem I knew onto the diagram:
a) Show that the train is going at 45 mph (for part A of the problem).
b) Show that the man is going at a constant speed no matter which way he decides to go.
3. Using the variables used in the distance formula (D=distance; S=speed; T=time).
4. Then I used the distance formulas to find the speed the man had to run in either direction in order to escape the train speeding towards him:
a) First based on my knowledge that the man was going S mph for D towards point A, I could use the Distance formula to calculate the time it takes for the man to run that distance. Time (T) = Distance (D) Speed (S)
T1 = x =
b) Next I repeated step 3a except with a distance of with the same constant speed S. For D, the Time (T2) =
c) Using the time in step 3b you can figure out the distance away from the end of the bridge the train is since you have the speed and distance in the distance formula, D1=S2*T2. Where D1 is the distance the train is away from point B, and moving at a speed S2=45mph. Substituting