Two trains leave stations
272
miles apart at the same time and travel toward each other. one train travels at
75
miles per hour while the other travels at
95
miles per hour. how long will it take for the two trains to meet?

It will take them 1.6 hours to meet. The formula for distance is d = rt, where d is distance, r is rate, and t is time. The only thing in common between the 2 trains is the time they meet. So set up the equation and solve it for time: t = d/r. Because the times are equal to one another, after we find the specifics for each train we can set them equal to one another. Train 1 travels a distance of x at a rate of 75. Because the total distance traveled is 272 miles, Train 2 travels a distance of 272 - x at a rate of 95. Distance over rate for each is x/75 for train 1 and 272-x/95 for train 2. Setting those equal to one another gives you x/75 = 272-x/95. Cross multiply to get 95x = 75(272-x). Doing that math gives you 95x = 20400-75x. Solving for x we get that x = 120. Now we need to use that 120 in our distance formula in place of the x's because time is equal to distance over rate (t = d/r, re,member?). For train 1, the time equation was t = x/75. Filling in 120 for x we get t = 1.6 hours. Let's do the same thing for train 2. The times better be the same because we decided in the beginning that time was the only thing the trains shared that was the same. t = 272-x/95 with a replacement of 120 for x gives you x = 1.6 hours