SOLUTION: two trains traveled in opposite directions from the same starting point. one train traveled 25 mph faster than the other one. after 4 hours they were 456 miles apart. find the rate

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Question 118390: two trains traveled in opposite directions from the same starting point. one train traveled 25 mph faster than the other one. after 4 hours they were 456 miles apart. find the rate of each train.
Answer by rcmcc(152) About Me  (Show Source):
You can put this solution on YOUR website!
To solve this question you must first find a linear equation.
Let the speed of the slower train equal (x)
the faster train is 25mph faster than (x) so train 2=(X)+25
Because 4 hours elapsed we can state that (4)(X) distance has occured for the slower train and (4)(x+25) has occured for the faster train.
Because we are looking for the total distance between them we can add them to find the total distance.
train x+train Y= XY
(4x)+(4y)=456
because y (faster train) is represented by x+25. substitute the value.
your linear equation is below
4(X)+(4)(x+25)=456
expand the brackets and simplify the equation and solve
4x+4x+100=456
8x+100=456
8x=356
x=44.5
so the slower train is traveling at 44.5mph and the faster one is traveling at 69.5.
You can test this by substituting the numbers into your equation (4x)+(4y)=456
(4)(44.5)+(4)(69.5)=456.
Solved.