Train A has a speed 15 miles per hour greater than that of train B. If train A travels 280 miles in the same time train B travels 250 miles, what are the speeds of the two trains?

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:

Train B:

 and setting them equal to each other because t = t:

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.

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step-by-step explanation:

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