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A freight train takes 4.5 hours longer to make a 420-mile journey than a passenger train. If the passenger train averages 30 mph faster than the freight train, how long does it take the passenger train to make the trip?
My teacher says the answer is 6 hours, but how do you set up this equation? I am very confused and have my midterm exam soon, if you can, please show your steps!! Thanks so much!
The key is in converting the words to equations, starting with what you want to know.
T = Trip time for passenger train (hours).
V = Speed of passenger train (mph; it's useful to parameterise yet not the solution).
=> Time of freight train = T + 4.5, speed = V - 30 (note passenger is *faster*).
Distance in both cases = 420 (miles)
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General equation for distance in constant velocity (or average): d = t * v
Plug each set of vales:
420 = T * V
420 = (T + 4.5) * (V - 30)
And solve for T & V. Check your final solution back in the two equations, as always.
Thanks sooo much!!