# Algebra

posted by .

A train leaves Danville Junction and travels north at a speed of 75 km/h. Two hours later, a second train leaves on a parallel track and travels north at 125 km/h. How far from the station will they meet?

I have no idea what the system of equations would be for this problem, or how to find the system of equations.

Once I have the system of equations, I should be able to solve it myself.

Thanks! :)

• Algebra -

I used to encourage my students to make a chart for these kind of problems
the rows of the chart are the different situations and the columns would be titled
D(distance) R(rate) and T(time)

............D ........R ......T
1st train: 75t ------ 75 ---- t
2nd train: 125(t-2)-- 125 --- t-2

didn't they travel the same distance?
so 125(t-2) = 75t

Notice I only used one variable, if your teacher insists that you use two of them,
define first time as x
the second time as y
then the difference in their times is 2
---> x - y = 2
and the second equation would be 75x = 125y

• Algebra -

Train 1 travels for time t at 75 km/hr
Train 2 travels for time (t-2) at 125 km/hr
they both go the same distance
distance = rate * time
therefore
75 t = 125 (t-2)

• Question -

You see, here's what I did.

I changed the "t" in the equation that both of you gave me (75t=125(t-2)) to an x so I could use elimination to solve the problem.

125x - 250 = 75x
+
75x = 125 y

That's where my problem comes along... it gets all weird and doesn't work. Is there another different equation I could have for the first equation in x and y form? Because I know that the second equation is basically the same as the first just w/ x's and y's, so is there another totally different equation?

Thanks! :)

• Algebra -

You can't just toss around x's and y's indiscriminately.

I gave you the corresponding equations if you have to use x and y

Of course things got weird.
you don't have an equation that states that the difference in their times is 2

• Algebra -

Oh, I kind of skimmed what you said and didn't notice the x-y=2... I'm sorry!

Thanks so much though! :)

P.S: Is the correct answer 375 miles away from the station, meaning x=5 and y=3?

• Algebra -

125x - 250 = 75x
+
75x = 125 y
------------------------
but what is y in your system?
You have just written the same fact twice.
To make a system of two equations you need to state two facts
first they go the same distance, at 75 for x hours and the other at 125 for y hours
that is your
75 x = 125 y
now the other fact you are given is
x = y + 2
multiply that by 75 to use elimination
75 x = 75 y + 150
so
0 = 125 y - 75 y -150
150 = 50 y
y = 3
then go back for x
x = y+2 = 5

## Similar Questions

1. ### Math

Train A and train B leave station going in opposite directions. Train B leaves 1/2 later than train A. Train B travels 80km/h faster than Train A. In 2 hours the trains are 3200KMs apart. How fast is each train traveling.. thank you
2. ### pre algebra

train A leaves a station at 1:15 PM,traveling 60 mph.Train B leaves the same station, in the same direction as train A,15 minutes later.If train B travels 90mphm when (clock time)will train B catch up to train A and how far down the …
3. ### Algembra

a train leaves a station and travels north at 85 km/hr. Four hours later, a second train leaves on a parrallel track and travels north at 125km/hr. How far from the station will they meet?
4. ### Algebra 2 (Distance Problem)

A train leaves Union Station for Central Station, 216 km away, at 9 A.M. One hour later, a train leaves Central Station for Union Station. They meet at noon. If the second train had started at 9 A.M., and the first train at 10:30 A.M., …
5. ### Math

A train leaves a station and travels north at a speed of 45mph. Four hours later, a second train leaves on a parallel track and travels north at 105 mph. How far from the station will they meet?
6. ### Algebra 2

at 2 pm a freight train leaves a station and travels at 42 km/h. at 11pm and express train leaves the same station on a parallel track and travels at 105 km/h in the same direction. how far from the station will they meet?
7. ### algebra

A train leaves a station and travels north at a speed if 50 mph. Five hours later, a second train leaves on a parallel track and travels north at 175 mph. How far from the station will they meet?
8. ### college algebra

A freight rain leaves a station and travels north at a constant rate of 60 mph. One hour later a passenger train leaves the same station traveling north on a parallel track at 80 mph. How long will it take for the passenger train to …
9. ### Mathematics

A train leaves station x and travels east at 30 kph. Two hours later,another train leaves the same station and travels in the same direction on a parallel track at 45kph. At what point will the faster train overtake the slower train?
10. ### math

A train leaves a station and travels north at a speed of 105 mph. Two hours​ later, a second train leaves on a parallel track and travels north at 135 mph. How far from the station will they​ meet?

More Similar Questions