SOLUTION: A freight train left New York City traveling north at a rate of 40 miles per hour. Two hours later, a passenger train left the same station traveling north over the same route at t

Algebra ->  Equations -> SOLUTION: A freight train left New York City traveling north at a rate of 40 miles per hour. Two hours later, a passenger train left the same station traveling north over the same route at t      Log On


   



Question 199109: A freight train left New York City traveling north at a rate of 40 miles per hour. Two hours later, a passenger train left the same station traveling north over the same route at the rate of 60 miles per hour. How many hours did it take the passenger train to overtake the freight train? (Only an algebraic solution will be accepted.)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
for freight train,
d+=+r%5B1%5D%2At%5B1%5D
For passenger train,
d+=+r%5B2%5D%2At%5B2%5D
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Given:
d is the same for both
r%5B1%5D+=+40 mi/hr
r%5B2%5D+=+60 mi/hr
t%5B2%5D+=+t%5B1%5D+-+2
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(1) d+=+40%2At%5B1%5D
d+=+60%2A%28t%5B1%5D+-+2%29
(2) d+=+60t%5B1%5D+-+120
Subtract (1) from (2)
(2) d+=+60t%5B1%5D+-+120
(1) -d+=-+40%2At%5B1%5D
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0+=+20t%5B1%5D+-+120
20t%5B1%5D+=+120
t%5B1%5D+=+6
I need to find t%5B2%5D
t%5B2%5D+=+t%5B1%5D+-+2
t%5B2%5D+=+6+-+2
t%5B2%5D+=+4
It took the passenger train 4 hrs to overtake the freight train