trains leave new york for boston every 40 min. the first train leaves at 5:20 a.m. what departure time is closest to 12:55 p.m.?
Three trains leave every 2 hours.
The tenth train leaves at 11:20 AM. The next will be at noon, 12:40 PM and 1:20 PM.
The 12:40 PM departure is closest
To find the departure time closest to 12:55 p.m., we need to calculate the number of minutes between 5:20 a.m. and 12:55 p.m. and divide it by 40 (the number of minutes between train departures).
Step 1: Convert 5:20 a.m. to minutes.
We know there are 60 minutes in an hour, so 5 hours (from 5 a.m. to 10 a.m.) would be 5 * 60 = 300 minutes. Adding the 20 minutes from 5:20 a.m., the total is 300 + 20 = 320 minutes.
Step 2: Convert 12:55 p.m. to minutes.
Again, we know there are 60 minutes in an hour, so 12 hours (from 10 a.m. to 10 p.m.) would be 12 * 60 = 720 minutes. Adding the 55 minutes from 12:55 p.m., the total is 720 + 55 = 775 minutes.
Step 3: Calculate the time difference.
To find the time difference between 5:20 a.m. and 12:55 p.m., subtract the minutes from Step 1 from the minutes in Step 2: 775 - 320 = 455 minutes.
Step 4: Divide the time difference by the frequency of train departures.
Since trains leave every 40 minutes, divide the time difference (455 minutes) by 40: 455 / 40 ≈ 11.375.
Step 5: Determine the number of train departures.
The decimal part of 11.375 represents the fraction of a train departure. We discard this fraction and focus on the whole number, which indicates the number of train departures. In this case, there have been 11 train departures.
Step 6: Calculate the departure time.
Multiply the number of train departures by the frequency of train departures (40 minutes) and add it to the initial departure time (5:20 a.m.): 11 * 40 = 440 minutes. Adding this to 5:20 a.m., we get a new departure time of 5:20 a.m. + 440 minutes = 9:40 a.m.
Therefore, the departure time closest to 12:55 p.m. would be 9:40 a.m.