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Okay so "The fast freight completed the trip in 10 hours while the slow freight needed 12 hours for the same trip. How long (distance) was the trip if the fast freight train was 10 kph faster than the slow freight?"

These are uniform motion problems at egual distance (which aren't difficult because I got all my other problems correct), but how am i suppose to solve for the distance? They don't give you a distance to start off with, do i make it up or is their a formula to find it?

All they gave me about distance was that the fast freight was "10kph" faster.


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Set up some equations for each train. Say the slow freight has velocity [itex]v_s[/itex] and the fast freight has velocity [itex]v_f[/itex].

d = v_s \cdot (12\,{\text{hours)}} \hfill \\
d = v_f \cdot (10\,{\text{hours)}} \hfill \\

Now, since the same distance was covered, you can set the two equations equal to each other, and distance "disappears":

v_s \cdot (12\,{\text{hours)}} = v_f \cdot (10\,{\text{hours)}}

And you know that [itex]v_f[/itex] = [itex]v_s + 10[/itex]

Now you can solve for either velocity.

- Warren
Thanks for the explenation

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