If a train leaves from....?

Question

Does anyone know if there is an actual equation used to figure out a question like...

If a train leaves from New York traveling 65 miles an hour and a train from chicago leaves, going toward the other train at 72 miles an hour, where will they meet? Or how long or whatever?

I've heard this question a ton, and I was wondering if there wa sa certain equation that could figure it out.

Answer 1

Yes there is. You have to use a distance equation like this one:
S = V(t) + D
where S is the position it will end up in
V is the velocity (speed) it travels at
t is the time it takes
and D is the displacement, or the distance from "zero" that it starts at

You can define point zero wherever you want. In this case I will say that "zero" is at New York. We need to know the distance between New York and Chicago to figure out this equation, which is 719 miles according to angelfire.com. So Chicago is at point 719 then. Here are the distance equations for the two trains:

New York: S = 65(t) + 0
Chicago: S = -72(t) + 719

The reason that Chicago has a negative velocity is because it is going from point 719 to point 0, which is in a negative direction according to how I chose to set up the equation.

These trains will meet each other when both of their S values are equal, so we will set New York's S equal to Chicago's S:

65(t) + 0 = -72(t) + 719

After we solve for t, we will know how long it took the two trains to meet each other.

65(t) + 72(t) = 719
137(t) = 719
t = 719/137 = 5.25

Since our velocity was measured in miles per hour, our t is measured in hours, so it took the trains 5.25 hours to meet.

Answer 2

Everything in life has an equation. Your question is too loose ended.
Where exactly in Chicago? Where in New York? Are they on the on the same track? Are they making any stops on the way?

If they are on different tracks they will never meet, yet they may pass each other.

You need to start with something easier and then apply the same principle.

Like: I have 5 pounds of feathers and 5 pounds of lead and 5 pounds of potatoes.
I'm standing on top of a 100 foot building.
I drop all 3 at exactly the same time.
Which one hits the ground first?

Answer 3

i dont know if there is a formula... but you do need to know the distance between the two cities.. and then just figure out... ok 72 mph... in 3 hours it goes 216 mph.. and so on with the other until you get the amount of miles added up to the total amount of miles the trip is... well good luck with that

Answer 4

Jen says the cities are 719 miles apart. Using distance = rate x time, both trains will meet when they have covered a total distance of 719 miles.

Let x = time it takes for trains to meet.
then 65x is distance covered by NY train, and 72x is distance covered by Chicago train.

65x + 72x = 719
137x = 719
x = 5.248 hours (5 hrs, 15 min.)
Distance covered by NY train = 65(5.248) = 341.12 miles
Distance covered by Chicago train = 72(5.248) = 377.856 miles

Answer 5

it all depends on how far apart they are.

Speed = Distance/Time

we have the speed, we have to find the time, but we don't know how far apart they are.

If Train A and Train B are x miles apart, Train A travels at y mph and Train B travels at z mph travelling toward each other, how long will it take the two to meet

Answer 6

yes, there are actual equations used to figure out that stuff.you can use a map that graphs miles on an x y axis. on that axis you would measure ( ) mph. when you've decided how fast each train will go you start using a pen or something that can mark where the trains are. then when they hit you can see where they hit