SOLUTION: Please help me put the word problem below in linear equations. Thank you so much in advance. Please help me. How do I go about this with the question? An express and local tr

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Please help me put the word problem below in linear equations. Thank you so much in advance. Please help me. How do I go about this with the question? An express and local tr      Log On


   

Question 148931: Please help me put the word problem below in linear equations. Thank you so much in advance. Please help me.
How do I go about this with the question?
An express and local train leave gray's Lake at 3 P.M. and head for Chicago 50 miles away. The express travels twice as fast as the local, and arrives 1 hour ahead of it. Find the speed of each train.
Found 3 solutions by checkley77, ankor@dixie-net.com, stanbon:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
LET THE TIME OF THE LOCAL TRAIN=50/X
LET THE TIME OF THE EXPRESS=50/2X
50/X=50/2X+1
50/X-50/2X=+1
(2*50-50)/2X=+1
(100-50)/2X=+1
50/2X=+1
2X=50
X=50/2
X=25 MPH FOR THE LOCAL
25*2=50 MPH FOR THE EXPRESS.
PROOF:
50/25=50/50+1
2=1+1
2=2

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
n express and local train leave Gray's Lake at 3 P.M. and head for Chicago 50 miles away. The express travels twice as fast as the local, and arrives 1 hour ahead of it. Find the speed of each train.
:
The time they left is irrelevant to the problem
:
Let s = speed of the local
then
2s = speed of the express
:
Write a time equation: Time = dist%2Fspeed
:
Express time + 1 hr = Local time
50%2F%282s%29 + 1 = 50%2Fs
Get rid of the denominators, mult equation by 2s; results:
50 + 2s = 2(50)
2s = 100 - 50
2s = 50
s = 50%2F2
s = 25 mph speed of the local
then
50 mph speed of the express
;
;
Check solution
50%2F50 + 1 = 50%2F25
1 + 1 = 2

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
An express and local train leave gray's Lake at 3 P.M. and head for Chicago 50 miles away.
The express travels twice as fast as the local, and arrives 1 hour ahead of it. Find the speed of each train.
---------------
Local Train DATA:
distance = 50 mi ; rate = x mph ; time = d/r = 50/x hrs.
-----------------------------------------
Express Train DATA:
distance = 50 mi ; rate = 2x mph ; time = d/r = 50/2x hrs.
-----------------------------------------
EQUATION:
local time - express time = 1 hr
50/x - 50/2x = 1
(50/x) - (1/2)(50/x) = 1
(1/2)(50/x) = 1
25/x = 1
x = 25 mph (speed of the local train)
2x = 50 mph (speed of the express train)
========================
Cheers,
Stan H.