Linear Equations dealing with motion

[kazuchan]

At 11AM a train traveling 57 mph leaves Chaney City for Atlantic City 543 miles south. At 1PM a train on a parallel track leaves Atlantic City for Chaney City and travels at 42 mph. At what time will they pass each other?

I have 57x+42y=543 and x+2=y
and I solved for x and y. I got x=51/11 and y=73/11 but now I do not know what do do from here. Can someone please help me? Thank you!

 

[JonF]

What are your x and y supposed to represent? There is no reason for 2 variables - this is how I would solve this problem:


You need to know how long it will take the trains to move 543 miles collectively. Let’s call 1:00pm time 0…

So train 1 moves 57mphs and starts 2 hours before time 0. So its distance would be 57(t+2).

Train 2 leaves at time 0 and travels 42 miles per hour so it would be 42(t+0) = 42(t)

So since trains are moving in opposite directions we need to know how long it will take them collectively to move 543 miles, so: 57(t+2) + 42(t) = 543

Once you find t that’s how many hours past time 0 (1:00pm) they will cross.

 

[kazuchan]

I got it. I had my second equation wrong. it should have been x=2+y. thanks for the help anyways.

 

[HallsofIvy]

Did you learn nothing from JonF's response? Writing "57x+42y=543" is meaningless if you don't say what "x" and "y" represent. No one here could help you without knowing that! We certainly could not say how to find "the time at which the trains pass" from x and y if we don't know what x and y represent!