SOLUTION: Mark is involved in a cross country run and starts down the path at his normal pace; he usually covers 12 m in 2.0 s. After tying his shoelace for 15 s, Frank discovers that he has

Question 1209809: Mark is involved in a cross country run and starts down the path at his normal pace; he usually covers 12 m in 2.0 s. After tying his shoelace for 15 s, Frank discovers that he has just given Mark a large lead. Nonetheless, Frank is faster at 6.5 m/s. Determine:
How long does it take Frank to catch Mark? (180 s)
If the race is 3 km in length, who finishes first and by what distance? (Frank, 140 m)

Answer by ikleyn(52760) (Show Source): You can put this solution on YOUR website!
.
Mark is involved in a cross country run and starts down the path at his normal pace;
he usually covers 12 m in 2.0 s.
After tying his shoelace for 15 s, Frank discovers that he has just given Mark a large lead.
Nonetheless, Frank is faster at 6.5 m/s. Determine:
(a) How long does it take Frank to catch Mark? (180 s)
(b) If the race is 3 km in length, who finishes first and by what distance? (Frank, 140 m)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

                    The solution for (a)


Mark' speed is 12/2 = 6 m/s;  Frank' speed is 6.5 m/s.

Let "t" be the time for Frank to catch Mark.


Equate distances for Mark and for Frank

     Mark      Frank

    6*(t+15) = 6.5*t.


Simplify and find t

    6t + 90 = 6.5t

    90 = 6.5t - 6t

    90 =   0.5t

    t = 90/0.5 = 180 seconds.


Frank will catch Mark in 180 seconds.

Solved.

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