word problem help?

Question

okay, first good explanation gets best answer..

Two trains leave Omaha, one traveling east and the other traveling west. If one is movine 20 mph faster than the other, and if after 4 hours they are 520 miles apart, how fast is each going?

Answer 1

velocity1=x
velocity2=x+20
4(2x+20)=520
(2x+20)=130
2x=110
x=55 MPH

Answer 2

One is traveling x mph.
The other is 20mph faster than x or x+20

Their relative speed is their combined speed. That is, it's as if one of them were standing still and the other was moving away from it. It's speed would be x+ (x + 20) or 2x + 20

The distance they traveled in 4 yours is 520.
The formula for distance (d) is d=rt where r is the rate of travel, and t is the time.

d = 520
t = 4
r = 2x+20

So, plugging what we have into the formula
d=rt
520=(2x+20)(4)

The problem now is to solve for x
First, multiply both sides by 1/4
130=2x+20
Second, add -20 to both sides
110=2x
Third, multiply both sides by 1/2
55 = x
The other train is 20 mph faster or 75.

To check this, see if 520 = (130)(4). It does... answers checked.

Answer 3

Assume one of them is moving x, then the other one is moving x+20. Since they are moving in opposite directions, it's as if one of them is standing still and the other one is moving the sum of their speeds or 2x+20. The distance the train would travel in 4 hours would be 4(2x+20) = 8x+80 which has to equal 520

8x + 80 = 520, 8x = 440, x = 55

So, the first train is going 55 and the second is going 75.

Answer 4

Start with distance = rate x time:

520=4r
r=130

Therefore, they are moving away from each other at a combined rate of 130 mph. Because they are moving away from each other, you add their speeds together to get the combined rate. Call Train A's speed x, in which case Train B's is x+20:

x+(x+20)=130
2x=110
x=55

Therefore, the trains are moving at 55 mph and 75 mph.