SOLUTION: A train leaves a station and travels north at 80 km per hour. three hours later a second train leaves on parallel tack and travel in the same direction at 120 km per hour. how far

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Question 162289: A train leaves a station and travels north at 80 km per hour. three hours later a second train leaves on parallel tack and travel in the same direction at 120 km per hour. how far from the station will they meet?
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!

Remember: Speed=distance%2Ftime, Working eqn
We 1st calculate the distance d%5B1%5D travelled of TR[1] after 3 hours:
Via working eqn,
S%5B1%5D=d%5B1%5D%2Ft%5B1%5D
d%5B1%5D=S%5B1%5Dt%5B1%5D=80%2A3=240km
After 3 hours, t%5B1%5D=t%5B2%5D, via working eqn we get
t%5B1%5D=d%5B1%5D%2FS%5B1%5D ----------------> EQN 1
t%5B2%5D=d%5B2%5D%2FS%5B2%5D ---------------->EQN 2
EQN1=EQN2
d%5B1%5D%2FS%5B1%5D=d%5B2%5D%2FS%5B2%5D
240%2F80=d%5B2%5D%2F120
3=d%5B2%5D%2F120
highlight%28d%5B2%5D=360km%29. Why highlighted? we'll see below:
.
how long it took TR%5B2%5D to travel 360km? Via EQN 2,
t%5B2%5D=360%2F120=3hours
In this span of ANOTHER 3 hours, how far TR%5B1%5D travelled? Via EQN 1,
t%5B1%5D=%28d%5B2%5D-d%5B1%5D%29%2FS%5B1%5D
t%5B1%5D=%28360-240%29%2F80=120%2F80=1.5hrs
So, total time travlled by TR%5B1%5D=3hrs%2B1.5hrs=4.5hrs;
So Total Distance travlled by TR%5B1%5D in 4.5 hrs:
via working eqn,
d%5B1.1%5D=S%5B1%5Dt%5B1.1%5D=80%2A4.5
highlight%28d%5B1.1%5D=360km%29. SEE highlighted, both are the same, and we'll meet at this distance.
Hope this helps.
Thank you,
Jojo