Distance = rate x time
The rate of the first train is 30
The rate of the second train is 50
If we let t represent the time of travel for the first train, then the time of travel for the second train will be t - 4 because it departed the station four hours later. We can now set up an inequality.
30t < 50(t - 4)
The value on the left represents the distance traveled by Train 1. The right side of the inequality is the distance traveled by Train 2. Now, let's solve.
30t < 50t - 200
-20t < -200
t > 10 We flip the inequality sign when dividing by a negative number.
So, ten hours after Train 1 left the station (at 3 p.m.) is when Train 2 will pass Train 1. Ten hours from 3 p.m. is 1 a.m.
Another way to view it is 6 hours after Train 2 left the station, it will pass Train 1. Why? Because the time traveled by Train 2 is t - 4, and 10 - 4 = 6. Again, six hours from 7 p.m., the time that Train 2 left the station, is 1 a.m.
