Question 815593: A freight train leaves the station traveling 30km/hr. One hour later, a passanger train leaves the same station on parellel track at 60km/hr. How far from the station does the passanger train overtake the frieght train?
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! s = d / t
d = s * t
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when the passenger train (p) leaves the station, the cargo train (c) has already traveled one hour:
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when p overtakes c, both trains have traveled the same distance from the station, but c has been traveling 1 hour longer than p.
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c at the overtake:
d = 30 / t
where t is the time of the overtake, measured from the time that c departed the station
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p at the overtake:
d = 60 / (t + 1)
where t is the time of the overtake, measured from the time that c departed the station
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c and p at the overtake:
d = 30/t = 60/(t + 1)
30(t + 1)/(t(t + 1)) = 60t/(t(t + 1))
60t/(t(t + 1)) - 30(t + 1)/(t(t + 1)) = 0
60t - 30(t + 1) = 0(t(t + 1))
60t - 30t - 30 = 0
30t = 30
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time of the overtake:
t = 1 hour after c departed the station
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Answer:
d = 30 / t
d = 30 km/hr / 1 hr = 30 km
so the overtake occurs 30 km from the station
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