SOLUTION: if one train leave the station traveling at 30 mph and another train leaves a half hour later traveling at 50 mph, when will they meet?

Question 446341: if one train leave the station traveling at 30 mph and another train leaves a half hour later traveling at 50 mph, when will they meet?
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
if one train leaves the station traveling at 30 mph and another train leaves a half hour later traveling at 50 mph, when will they meet?
-----------------
Slower train DATA:
rate = 30 mph ; time = x hrs ; distance = 30x miles
----
Faster train DATA:
rate = 50 mph ; time = x-(1/2) hr; distance = 50x-25 miles
----
Equation:
distance = distance
30x = 50x-25
25x = 25
x = 1 hr
---
They will meet one hr after the slower train left the station.
==========================
Cheers,
Stan H.

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
How much of a head start does the 1st train get?

mi.
Write equations for both with equal to the time
from when the 2nd train leaves to when they meet,
and = distance the 2nd train has to go to
where they meet
1st train:
(1)
2nd train:
(2)
------------
(1)
(1)

They will meet 45 minutes after the 2nd train leaves
and 1 hour 15 minutes after 1st train leaves
check:
(1)
(1)
(1)
(1)
and
(2)
(2)
(2)
OK
RELATED QUESTIONS
Train A leaves a station traveling at 25 mph. One half hour later Train B leaves the same (answered by Edwin McCravy)
Train A leaves the station traveling at noon traveling 30 mph. Train B leaves the same... (answered by jorel1380)
Train A leaves a station traveling at 40 mph. Six hours later, train B leaves the same... (answered by solver91311)
Train A leaves a station traveling at 20 mph. Four hours later train B leaves the same... (answered by ankor@dixie-net.com)
a train leaves the station traveling west at 50 mph. One hour later a second train... (answered by checkley77,ankor@dixie-net.com)
There is a train station located at some point on a circular track of radius 30/pi miles. (answered by kev82)
A train leaves Watsonville at noon traveling north at 44 mph. One hour later, another... (answered by Alan3354)
A TRAIN LEAVES D.C. AT NOON TRAVELING NORTH AT 44 MPH. ONE HOUR LATER, ANOTHER TRAIN... (answered by mananth,nyc_function)
a train leaves Havre at 5:30 and heads west at 40/mph. Half an hour later another train... (answered by checkley71)