3.2 Time, Addition, and Subtraction
Activity: Train Journeys
To get to a very important meeting you can travel by train, leaving at 9:35 a.m. and arriving at 11:10 a.m. The ticket costs $48.30, but you have a refund voucher for $15.75 following the cancellation of a train on an earlier journey. You know from experience that the conductor won’t let passengers leave the train for an additional ten minutes after arriving at the station.
How long will the journey take, and how much money will you have to pay for the ticket if you use the entire refund voucher?
Start by taking out all the information from the question—this should help to make the problem clearer.
To determine the length of time, you could figure out how many minutes you will have been on the train by 10:00 a.m., and then add up the time until you reach 11:10 a.m. Don’t forget the extra ten minutes the conductor requires.
To determine your total cost, write down the ticket cost and subtract your refund. Use the vertical format, where your digits are lined up by place value and the decimal points are aligned.
Working with times can be tricky, because you have to remember that there are 60 minutes in an hour, so you are not working with the simple decimal system. Imagine a clock and say, “From 9:35 to 10:00 is 25 minutes; 10:00 to 11:00 is an hour, and 11:00 to 11:10 is an extra ten minutes. So the journey time is 1 hour and 35 minutes, assuming the train runs on time. Then the conductor requires waiting an extra ten minutes, giving a grand total of 1 hour and 45 minutes.”
Now you have one more step:
To find out how much you will have to pay for the ticket, you need to subtract $15.75 from $48.30. Think it out this way:
“Doing a formal subtraction in my head isn’t easy, so I’ll work up from $15.75. Adding on 25 cents gives me $16.00, then I need $32 to get to $48.00 and another 30 cents to reach $48.30. So, the total I have to pay is $32 plus 25 cents plus 30 cents, or $32.55.”
Now you have learnt about addition and subtraction, and some ways of tackling problems involving these, let’s investigate the two other operations: Multiplication and division.
Remember to continue to think about how your studying is going and to use your math notebook to jot down your thoughts.