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.
At what time does the second bus catch up with the first bus?
Enter your answer, separating hours and minutes with a colon, in the box.
To find the time the second bus catches up with the first bus, we need to determine the time it takes for the second bus to travel the same distance as the first bus.
Since the first bus leaves at 4:00 p.m. and travels at 40 miles per hour, it will have traveled for 1 hour when the second bus leaves at 5:00 p.m. (5:00 p.m. - 4:00 p.m. = 1 hour).
In that 1 hour, the first bus will have traveled 40 miles (40 miles/hour * 1 hour = 40 miles).
To catch up to the first bus, the second bus needs to cover the same 40 miles.
Traveling at a speed of 60 miles per hour, the second bus will take 40 minutes to travel 40 miles (40 miles / 60 miles/hour = 0.667 hours or 0.667 * 60 minutes = 40 minutes).
Therefore, the second bus catches up with the first bus at 5:40 p.m. (5:00 p.m. + 40 minutes = 5:40 p.m.).