SOLUTION: Hello tutor, i need help with this problem: (may you please show some steps?) Two trains leave Sacramemto at the same time. One travel East at 40mph. The other traveled West at 60

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Question 553429: Hello tutor, i need help with this problem: (may you please show some steps?)
Two trains leave Sacramemto at the same time. One travel East at 40mph. The other traveled West at 60mph.Write amd solve a system of linear equations that can be used to determine when the trains are 280 miles apart.
Thank You!!!!
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
x equals the distance traveled by the first train.
y equals the distance traveled by the second train.
the general equation is rate * time = distance.
you have a series of equations.
first equation is:
x + y = 280
second equation is:
40z = x
third equation is:
60z = y
z is equal to the time which needs to be the same for both trains because they will be 280 miles apart at the exact same time.
your 3 equations are:
x + y = 280
40z = x
60z = y
if you look at these 3 equations, you can see that you can replace x and y in the first equation with 40z and 60z from the second and third equations because they are equivalent.
you get:
40z + 60z = 280
combine like terms to get:
100z = 280
divide both sides of the equation by 100 to get:
z = 2.8
this says that the trains should be 280 miles apart in 2.8 hours.
let's see if that's true.
the first train travels 2.8 hours at 40 miles per hour for a distance of 2.8 * 40 = 112 miles.
the second train travels 2.8 hours at 60 miles per hour for a distance of 2.8 * 60 = 168 miles.
if you add 112 and 168 you get a total of 280 miles.
it works out ok and the answer is 2.8 hours.
in this particular case, we used the process of substitution to narrow down the unknown variable from 3 to 1 and we were left with one equation in one unknown that could be solved.