Question 32426: I can't seem to take out the equations from the from the word problem and I don't remeber the steps on how to slove it.
3 trains—1 eastbound, 1westbound, and 1northbound—leave a city at the same time. The speed of the northbound train is 20 mph greater than the speed of the eastbound train After 7 hours, the distance between the westbound train and the eastbound train is 700 miles. Twice the speed of the westbound train is 90 mph more than the speed of the northbound train. . Find the speed of the 3 trains.
This is what I did:
3 trains—1 eastbound, 1westbound, and 1northbound—leave a city at the same time.
Eastbound = X, westbound = Y, northbound = Z.
The speed of the northbound train is 20 mph greater than the speed of the eastbound train
20 >X=Z
After 7 hours, the distance between the westbound train and the eastbound train is 700 miles.
Y-X=700 miles
Twice the speed of the westbound train is 90 mph more than the speed of the northbound train.
2Y=90+Z
Find the speed of the 3 trains.
Answer by mukhopadhyay(490)   (Show Source):
You can put this solution on YOUR website! Eastbound = x mph
Nothbound = x+20 mph
Westbound (if z)=> 2z = (x+20)+90; => z = (x+110)/2 mph;
..................................
Eastbound in 7 hours = 7/x miles
North bound in 7 hours = 7/(x+20) miles
Westbound in 7 hours = 14/(x+110) miles
....................................
East and West travel on the opposite direction
=> Distance between these two trains is the sum of the distances covered by them
=> 7/x + 14/(x+110) = 700
=> 1/x + 2/(x+110) = 100
=> 3x+110 = 100(x)(x+110)
=> 3x+110 = 100x^2 + 11000x
=> 100x^2 + 100097x - 110 = 0
..... The roots of the above equation will come in fracions; use quadratic formula to find the positive root. Once x is found, you will be able to find the speed of all trains.
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