William wants to travel to Paris by train. He needs to arrive in Paris by 5:30 pm. Circle the latest time that William can leave London.
To help solve this problem, we’re provided with a timetable. It shows information for seven different trains. The first column shows us what time each train leaves London. And in the second column, we can see what time they arrive in Paris. We’re told that William needs to arrive in Paris by 5:30 pm. So we need to look at this second column to find out which trains he can get on.
If William wants to arrive in Paris by 5:30 pm, we know he needs to catch a train that gets there before or exactly at that time. It’s no good arriving later than 5:30. But where would 5:30 be in the second column? The times seem to be written with larger numbers like 15, 16, 17, and so on. That’s because they’ve been written as 24-hour clock times.
This means we don’t have to write am or pm. If a time is at pm time, we just add 12 to the number of hours. So for example, one o’clock pm can be written as 13:00 hours because one plus 12 equals 13. So if William needs to arrive in Paris by 5:30 pm, we’re looking for the 24-hour clock time 17:30 because five plus 12 equals 17.
Which of the trains will get William into Paris by 17:30? 17:53 is later than 17:30. So William shouldn’t get this train or any of the trains after it. 17:26 is before 17:30. So William could catch this train and he could catch any of the trains before it. There are four possible trains that William could catch.
Our problem asked us to circle the latest time that William can leave London. We already know that he can catch any of the first four trains if he wants to get there by 17:30. The latest of these trains is the last one of the four. And so, the latest time that William can leave London is 14:01.
To solve the problem, we needed to convert a 12-hour clock time into a 24-hour clock time. Once we’ve done that, we can see that there were four possible trains that would get William to Paris by 5:30 pm or 17:30.
So the latest time that William can leave London is 14:01.