Help with math word problem please? urgent! ?

Question

here's the problem:

two trains start at the same place, traveling in opposite directions for 6 hours. after 3 hours they are 414 miles apart. how fast is each traveling if the rate of one train is 8 mph faster than the other?

any help is appreciated, thank you!

Answer 1

k well what i  did was i took 414 divided it by 6 then i got 69 . so i took away 8 and added it to the other so i got 61 and 77 mph not shur if its right but i think it is  

Answer 2

First, it's a good idea to figure out how far they travel in ONE hour.

414/6 = 69 miles in one hour

So the combined velocity would be 69mph

So

s(1) = the speed of the first train

s(2) = the speed of the second train

We know that

s(1) + s(2) = 69

s(1) = s(2) + 8

We can substitute

(s(2) + 8) + s(2) = 69

2s(2) + 8 = 69

2s(2) = 61

s(2) = 30.5mph

s(1) = 69 - 30.5

s(1) = 38.5mph

EDIT:

Okay, scratch my answer - I didn't read the question right and used 6 hours instead of 3

Answer 3

Train 1 is going V mph.

Train 2 is going V+8 mph.

So, 3 hours at V, plus 3 hours at V+8 equals 414 miles.

3(V+(V+8)) = 414

V = 65 mph and V+8 = 73 mph

The 6 hour data is irrelevant to the calculation.

Answer 4

414 miles apart in 3 hours implies a relative speed of 138 mph

let x be the speed of the slower train.

x + x + 8 = 138

2x = 130

x = 65 mph

The slower train is moving at 65 mph

The faster train is moving at 73 mph.

Checking

3 hours * 65 mph = 195 miles

3 hours * 73 mph = 219 miles

219 miles + 195 miles = 414 miles  CHECK

Answer 5

R1 is the rate the first train is moving. R2 is the second train.

R1 = R2 + 8

3*R1+3*R2 = 414

3*(R2 + 8)+3*R2 = 414

6*R2 = 414-3*8

R2 = 65 mph

R1 = 73 mph

Check

3*65+3*73=414

The 6 hours in the first line is a red herring and you don't need it. You can also check your equations by running just the units

hrs + hrs = hrs

mi/mph =hrs

Answer 6

a and b are the speeds of the trains

distance= speed * time

a mph=b mph+8

3hr*(b)+ 3hr*(b+8)=414

then solve:

3b+3b+24=414

            -24    -24

6b=390

/6    /6

b=65

a=b+8     so, a=73

Final answer: 65mph and 73mph

Answer 7

i am guessing, well hoping that they are going at a constant velocity.

(3x+8) + 3x= 414  solve this and you'll get your answer.

btw when you find x here, that is giving u the trains peed of the slower one... so all you need to do to find the faster one is add 8 mph to it.

Answer 8

Ok this is what you do:

The first train will be variable x and the second will be x + 8

414 = 3x +3(x+8)

390 = 6x

x = 65

The two trains are going 65 mph and 73 mph.

Answer 9

If they went 414 miles together in 3 hours. One train is 8 mph faster.  Cut 414 in half which gives you 212 per train. One train is 8 faster per hour for 3 hours equal 24.      212 minus 24 equals 188.

Possibly you have one train that is traveling at 62.66 mph while another is traveling at 8mph faster at about 70.66mph

I can't 100% garantee this answer but it's really close