Two buses are traveling to a state park. one bus leaves the terminal at 4: 00 p. m. and travels at 40 miles per hour. the second bus leaves the terminal at 5: 00 p. m. and travels at 60 miles per hour. how much time passes until the second bus catches up with the first bus?

The 2nd bus will catch up to the 1st bus after 2 hours. For this problem, the value t will be the time since the 2nd bus started traveling. So let's create a couple of expressions to indicate the distance each bus travels at time t First bus is traveling at 40 mph and has a 1 hour head start, so it has a 40 mile lead. The distance traveled at t time is 40t + 40 The second bus is traveling at 60 mph, so its equation is 60t Now let's set the two equations equal to each other and solve for t 40t + 40 = 60t 40 = 20t 2 = t So the 2nd bus will catch up to the 1st bus after traveling for 2 hours.