Question

Two trains leave the station at the same time, one heading west and the other east. The westbound train travels at 85 miles per hour. The eastbound train travels 105 miles per hour. How long will it take for the two trains to be 456 miles apart? Do not do any rounding.​

Answer 1

Answer:

Step-by-step explanation:

We'll make a table for this since we have 2 different trains for which we have formulas. We'll use the distance = rate * time formula, but we have to use it twice because we have 2 trains, then we have to come up with an equation that incorporates both of the distances of the 2 trains to come up with a time. Easy.

                      d           =          r         *          t

East train

West train

Now we can fill in. We know that the rate of the east train is 105 and the rate of the west train is 85, so we fill that in:

                     d           =            r         *           t

East train                               105

West train                               85

The time is what we are looking for, so that is the unknown for each train:

                        d          =          r         *           t

East train                               105                   t

West train                               85                   t    

Since the formula is d = rt, we will multiply the rates of each times the time of each and fill in accordingly:

                              d           =             r             *           t

East train          105t                      105                         t

West train           85t                       85                        t

Here's an illustration to the best of my abilities in this forum:

<------------------------------|----------------------->

            85t                          105t

|----------------------456 miles-------------------|

The illustration is supposed to show you that the distance between the trains (456 miles) is found by adding the 2 distances together and solving for t:

85t + 105t = 456

190t = 456 so

t = 2.4 hours