help with algebra problem?

Question

please please please include how you got the answer:
A train leaving traveling east at 80 miles per hour. An hour later, another train leaves east on a parallel track at 120 miles per hour. how far from the station will the trains meet?

Answer 1

240 miles

first write the equation for how far the first train has traveled in time h (in hours)

a = 80*h

second write the equation for how far the second has traveled in time h. (remember it didn't travel at all for the first hour)

b = 120 * (h-1)

so they will meet when they are equal
80*h = 120 * (h-1)
80*h = 120h - 120
120 = 40h
3 = h
so they will meet in 3 hours (that's 3 hours from the first train starting).

but the question was how far from the station -- that's 3 hours * 80 mph = 240 miles.

double check: the second train traveled for just 2 hours * 120 mph = 240 miles. right!

Answer 2

Train A:
Speed 80 mph
Distance = 80 miles after 1 hour

Train B:
Speed = 120 mph

RELATIVE speed of train B to train A = 40 mph

Question then becomes how long before trains pass?
t = 80 / 40 h
t = 2 h
d = 2 x 120 miles
d = 240 miles

Answer 3

This intuitive. It doesn't take algebra.

Their relative speed, that is, the speed at which they're closing is 120-80=40. That is, the second train is gaining 40 miles an hour. Doesn't make any difference that one's traveling in the same direction as the other.

At the end of one hour, the train traveling 80 mph traveled.... 80 miles. That's how many miles they have to go to get together.

At 40 miles per hour how long would you guess it would take to travel 80 miles?. Ok, how far would a train traveling at 120 mph travel in that time?

If you want algebra...

The distance the slow train travels after the first hour is 80t
The distance the fast train travels after it starts at the end of the first hour is 120t... 120t is 80 longer than 80t, or.

120t = 80t + 80

Add -80t to both sides
40t=80

The train will have traveled 120t when it catches the other train.

See it even works out in algebra...

Answer 4

Let the position of the slower, 80 mph train be denoted by A.
Let the position of the other train be denoted by B.
Let time after the faster train leaves be denoted by t.
We are therefore looking for t where
A = B
from the problem statement this becomes
80 + 80t = 120t
since the first train went 80 miles in the hour before the second train started
solving for t:
40t = 80
t = 2
Then plug back in this value for t on either side to obtain your answer:
80 + 80(2) = 80(3) = 240
120(2) = 240
Therefore the trains meet 240 miles east from the station.

Answer 5

The point at which they meet, is when the two trains are at the same location.

The first train is traveling 80 mph, for x hours.
The second train is traveling 120 mph, for x - 1 hours (it leaves an hour later from the first)

Now, set them equal to each other, to find how long it takes. You will notice the hours and miles cancel out on each side.

(80 mph)(x hr) = (120 mph)(x - 1 hr)
80x = 120x - 120
-40x = -120
x = 3

So, the first train traveled 3 hours and the second traveled 2 hours. Now, you have to find how many miles this takes.

(80 mph)(3 hr) = 240 miles

They were 240 miles away from the station.

Answer 6

You can solve this with basic physics.

the equation of motion for the first train can be
d=80t, t>0
the equation for the second train is then
d=120(t-1), t>1

find the time of intercection by equating:
80t=120(t-1)
0=40t-120
t=120/40=3 hours

now you know that they intercect after 3 hours, to find the distance traveled in that time substitute t=3 into either one of the origional equations:
d=80*3=240miles
as a check, sub into the second equation also:
d=120(3-1)=240 miles

Answer 7

The first train has been traveling for one hour so it's 80mph*1hour=80miles away from the station. If you subtract the first trains speed from the second you get 120-80=40 which is the speed at which the distance between them is shrinking. Since they are 80 miles away they will meet in 80miles* 1hours/40miles=2hours so how far can the second train go in 2 hours? 120mph*2hours=240 and that is your answer.

Answer 8

240 mi

since
v_1 = 80
and
v_2 = 120

* t_e means elapsed time
then the equation is
(v_1)(t+t_e)=(v_2)(t+t_e)
so
(80)(t+t_e)=(120)(t+t_e1)
t_e = 1
t_e1 = 0
(80)(t+1)=(120)(t+0)
80t+80=120t
120t-80t=80
40t=80
t=2
and, i guess you know that s=d/t
so
v_1=d/2
80=d/2
but since the train left 1 hour before you have to add t+1
80=d/3
d=3*80
240=d
so
d=240
voila!

Answer 9

although this is no help I'm in algebra1 and its hard to so yeah help is what WE need!

Answer 10

prime factor each number and find the GCF

80=2x2x2x5

120=2x2x2x3x5
--------------------------------
GCF=2x3x5=30miles