Question

Can somebody please help me with 3 and 5. Please don’t answer if you are not sure. 17 points

Answer 1

The Pyth. Thm. tells us the following:  (hypo)^2 = (leg 1)^2 + (leg 2)^2.
Here the hypo is 75 miles.  One train traveled x miles and the other x+10 miles.

applying the Pyth. Thm., 

x^2 + (x+10)^2 = 75^2

which becomes   x^2 + x^2 + 20x + 400 = 5625, or
                               2x^2 + 20x - 5225 = 0.

Choose a method easy for you that will lead to a solution (x-value).
Using "completing the square," I obtained x= 47.8 miles and x = 57.8 miles.  I

It's very important to check one's work.  Suppose x = 47.8 miles.  Then x+10 = 57.8 miles.

47.8^2 + 57.8^2 = 75^ must be true.  Is it?

2284.84 + 3340.84           5625
          5625.6      is approx equal to 5625.  Close enough.

The first train traveled 47.8 miles and the second 57.8 miles.