a train and a bus leave at 10:00 a.m. from towns 45 mi apart. they travel toward each other. the bus travels at 40 mph. the train travels at 50 mph. at what time do they meet?

Their combined speed is 90 mi/hr, so it takes them 1/2 hour to cover 45 miles.

To find out at what time the train and the bus meet, we need to determine the time it takes for them to cover the combined distance of 45 miles.

Let's break down the problem and find the time taken by each vehicle to cover the distance.

The bus is traveling at a speed of 40 mph, so we can use the formula:

Time = Distance / Speed

For the bus:
Time taken by the bus = 45 miles / 40 mph = 1.125 hours

Similarly, the train is traveling at a speed of 50 mph.

Time taken by the train = 45 miles / 50 mph = 0.9 hours

Now, we need to find the total time taken by both the bus and the train to meet. We can do this by adding their individual times:

Total time = Time taken by the bus + Time taken by the train
Total time = 1.125 hours + 0.9 hours = 2.025 hours

Since we know that both the train and the bus left at 10:00 a.m., we can find the meeting time by adding the total time to the initial departure time:

Meeting time = 10:00 a.m. + 2.025 hours

To convert the decimal part into minutes, multiply it by 60:

Meeting time = 10:00 a.m. + 2 hours + (0.025 * 60 minutes)
Meeting time = 10:00 a.m. + 2 hours + 1.5 minutes
Meeting time = 12:01.5 p.m.

Therefore, the train and the bus will meet at approximately 12:01.5 p.m.