Question 296691
Three trains one eastbound, one westbound, and one northbound leave a city at the same time. 
let e = eastbound train speed
let w = westbound train speed
let n = northbound train speed
:
The speed of the northbound train is 10 miles per hour greater than the speed of the eastbound train.
n = (e+10)
:
After 5 hours, the distance between the westbound train and the eastbound train is 450 miles.
5(e+w) = 450
5e + 5w = 450
simplify, divide by 5
e + w = 90
:
Twice the speed of the westbound train is 50 miles per hour more than the speed of the northbound train.
2w = (n+50)
Replace n with (e+10) from the 1st equation,
2w = (e+10) + 50
2w = e + 60
-e + 2w = 60
:
Use elimination with the 2nd equation 
-e + 2w = 60
 e + w = 90
------------------Addition eliminates e
3w = 150
w = 50 mph is westbound train speed
:
Find e using equation: e + w = 90
e + 50 = 90
e = 90 - 50
e = 40 mph is eastbound train
:
find n using equation, n = e + 10
n = 40 + 10
n = 50 mph is northbound train
:
check solution in the equation 5(e + w) = 450
5(40 + 50) = 450
5(90) = 450
:
Summarize: e=40, w=50, n=50