Answer:
Step-by-step explanation:
Let's make a table to keep track of the info.
d = r * t
Train A
Train B
Now we just need to fill it in! Let's look at the rates first, since that's the first bit of info given. Train A is going 15 miles per hour faster than Train B, but because we don't know how fast either is going, we will say that the rate of B is r, and the rate of A then is r + 15. Let's put that in the table.
d = r * t
Train A r + 15
Train B r
The distance Train A travels is 280 and the distance Train B travels is 250:
d = r * t
Train A 280 = r + 15
Train B 250 = r
We're getting there. We just need the time now. We don't have it, but we do know they left at the same time, t, so
d = r * t
Train A 280 = r + 15 * t
Train B 250 = r * t
The distance formula is d = rt, as illustrated in the way the table is set up, so let's get the distance formula for each train.
Train A: 280 = t(r + 15)
Train B: 250 = rt
Can't do much with that right now, but let's think about equality here for a minute. If the time is the same for both trains, then
t for Train A = t for Train B
Let's solve each of those distance equations for t and set them equal to each other:
Train A:
[tex]t=\frac{280}{r+15}[/tex]
Train B:
[tex]t=\frac{250}{r}[/tex] and setting them equal to each other because t = t:
[tex]\frac{280}{r+15} =\frac{250}{r}[/tex]
Cross multiply to get
280r = 250r + 3750 and
30r = 3750 so
r = 125
Train B is going 125 mph and Train A is going 140 mph. A bit fast, if I do say so myself.
