Question 296691: Three trains one eastbound, one westbound, and one northbound leave a city at the same time. The speed of the northbound train is 10 miles per hour greater than the speed of the eastbound train. After 5 hours, the distance between the westbound train and the eastbound train is 450 miles. Twice the speed of the westbound train is 50 miles per hour more than the speed of the northbound train. Find the speeds of the three trains.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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
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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
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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
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