SOLUTION: a and b are two station 300 km apert.Two train start simultaneously from a and b, each to the opposite station .The train from a reaches b 9 hours , the train from b reaches a 4

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Question 389044: a and b are two station 300 km apert.Two train start simultaneously from a and b, each to the opposite station .The train from a reaches b 9 hours , the train from b reaches a 4 hours after they meet, Find the rate at which each train travels? slove the problem.
Found 2 solutions by Fombitz, jrfrunner:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Rate*Time=Distance
R%2At=D
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D=300km
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R%5B1%5D%2At=300
R%5B1%5D%2A9=300
R%5B1%5D=300%2F9=100%2F3 kph
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R%5B2%5D%2A4=300
R%5B2%5D=75kph

Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
The trains meet somewhere between station a and station b
--
let train 1 "from" station a
let train 2 "from" station b
let d1=distance train 1 travels after meeting train 2
let d2=distance train 2 travels after meeting train 1
let r1=rate of train 1
let r2=rate of train 2
let t=time when trains meet
distance =rate * time or d=r*t
==
from meeting point to station a: train 1 has travelled r1*t
and train 2 will travel 4 hours to get to station a or r2*4
so... r1*t = r2*4
--
likewise
r2*t=r1*9
--
solving for t: r2*4/r1=t and r1*9/r2=t
4*r2/r1=9*r1/r2
4r2^2=9*r1^2 (cross multiply)
2*r2=3*r1
2*r2/3=r1
--
we also know that the total distance is 300, so
d1+d2=300
4*r2+9*r1=300
4*r2+9*(2*r2/3)=300
4*r2+6r*2=300
10*r2=300
r2=30
r1=2*r2/3=20