SOLUTION: Pls. help me with this word problem: The distance from NYC to a midwestern city is 1080 miles, and the time taken by the fastest train is 11 hours longer than the time taken by an

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Question 578575: Pls. help me with this word problem: The distance from NYC to a midwestern city is 1080 miles, and the time taken by the fastest train is 11 hours longer than the time taken by an airplane. If the train is used for the first third of the journey and the plane for the last two thirds, the time taken for the whole trip is 7 2/3 hours. Find the rate of each.
Thank you for your help, I am just helping my son out with these problems and I am stumped.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
whole distance
let time taken by plane be x hours
train takes x+11 hours
speed of plane = 1080/x
train takes 11 hours more
so speed of train = 1080/(x+11)
distance traveled by train and plane
distance traveled by train = 1/3 * 1080 = 360 miles
distance traveled by plane = 2/3 1080 = 720 miles
Time
Time taken by plane + time taken by train = 7 2/3 hours = 23/3 hours
t = d/r
360/(1080/(x+11)) + 720/(1080/x) = 23/3
(360(x+11))/1080 + 720x/1080 = 23/3
(360x+3960 +720x)/1080= 23/3
1080x+3960 = 23*1080/3
1080x+3960 = 23*360
1080x+3960 = 8280
1080x= 4320
x= 4
time taken by plane to go 1080 miles = 4
distance = 1080
speed = 1080/4 = 270 mph--- plane

speed of train = 1080/(x+11)
= 1080/15
=72 mph speed of train
m.ananth@hotmail.ca
have I walked you through