Yes, yes, I know I just blogged about the benefit of more "pure math" and somewhat less "real life application", but this was just too good a problem to give up, so here goes...
Recently, Ms. Teschow was invited by the teacher federation to present a math workshop for teachers in London, Ontario. Since Ms. Teschow lives in Toronto and teaches in Mississauga, she decided that the most efficient way to travel would be by train.
She called to inquire about train tickets to London. As it turns out, the train that leaves Toronto Union Station for London makes a stop in Oakville, not too far from Mississauga, and on the way to London.
Recently, Ms. Teschow was invited by the teacher federation to present a math workshop for teachers in London, Ontario. Since Ms. Teschow lives in Toronto and teaches in Mississauga, she decided that the most efficient way to travel would be by train.
She called to inquire about train tickets to London. As it turns out, the train that leaves Toronto Union Station for London makes a stop in Oakville, not too far from Mississauga, and on the way to London.
In an attempt to save the federation some money, Ms. Teschow decided to teach in her classroom in the morning, and then go to the Oakville train station at lunch to catch the 12:40 p.m. train to London, where she would be presenting the workshop later that afternoon. (Her plan was to head back home toToronto on the train later that evening, after the workshop was over.)
Unfortunately, there was a miscommunication with the travel agent booking the train ticket, and the outbound ticket sent to Ms. Teschow was booked to leave from Toronto Union Station!
Since Ms. T would be teaching in Mississauga until 11:30, and the train would be departing Union at 12:15 p.m., there was no way she would make it. But when she called the train company to see about getting her boarding pass changed to Oakville, the person on the phone told Ms. Teschow that she would have to pay a fee of $25 to have her ticket changed! Since Oakville is closer to London than Toronto is, Ms. Teschow didn't think she should have to pay extra, so she argued with the person on the phone, and was told that although the Oakville-->London ticket was about $3 cheaper than the Toronto --> London ticket, because of the change fee, it would still end up costing more in the end.
Frustrated, Ms. Teschow decided to take her chances, and just go to Oakville the next day at lunch to see what would happen there in person.
As it turned out, the nice lady at the Oakville train station said "don't worry about it, you can get on here, just explain to the train attendant that there was a mix up with the ticket". Whew! So Ms. Teschow boarded the train and sat down at her computer to put the finishing touches on her presentation.
Unfortunately, there was a miscommunication with the travel agent booking the train ticket, and the outbound ticket sent to Ms. Teschow was booked to leave from Toronto Union Station!
Since Ms. T would be teaching in Mississauga until 11:30, and the train would be departing Union at 12:15 p.m., there was no way she would make it. But when she called the train company to see about getting her boarding pass changed to Oakville, the person on the phone told Ms. Teschow that she would have to pay a fee of $25 to have her ticket changed! Since Oakville is closer to London than Toronto is, Ms. Teschow didn't think she should have to pay extra, so she argued with the person on the phone, and was told that although the Oakville-->London ticket was about $3 cheaper than the Toronto --> London ticket, because of the change fee, it would still end up costing more in the end.
Frustrated, Ms. Teschow decided to take her chances, and just go to Oakville the next day at lunch to see what would happen there in person.
As it turned out, the nice lady at the Oakville train station said "don't worry about it, you can get on here, just explain to the train attendant that there was a mix up with the ticket". Whew! So Ms. Teschow boarded the train and sat down at her computer to put the finishing touches on her presentation.
While eating her dinner and looking out the window on the train later on, Ms. Teschow couldn't help but wonder if it might have been cheaper for everyone if she had just taken the whole day off.
So here's the problem:
IF MS. T ACTUALLY HAD TO PAY THE $25 CHANGE FEE FOR THE TICKET, WOULD IT HAVE BEEN LESS EXPENSIVE FOR MS. T TO TAKE THE WHOLE DAY OFF WORK, INSTEAD OF JUST HALF A DAY?
Some numbers you might need to solve the problem:
BONUS QUESTION #1:
When Ms. Teschow looked online for the information, she discovered that in fact it was NOT $25, but 25% of the original fee that is supposed to be charged for a change in booking. Does this make a difference to the above problem? Explain your thinking.
BONUS QUESTION #2:
The teacher federation has a discount agreement with the train company of approximately 10%. How does this affect the overall price in the other problem(s)?
Happy calculating! :-)
So here's the problem:
IF MS. T ACTUALLY HAD TO PAY THE $25 CHANGE FEE FOR THE TICKET, WOULD IT HAVE BEEN LESS EXPENSIVE FOR MS. T TO TAKE THE WHOLE DAY OFF WORK, INSTEAD OF JUST HALF A DAY?
Some numbers you might need to solve the problem:
- Substitute teacher costs for half a day (approx) - $135
- TTC fare to get from Ms. T's home to Union Station - $3.25
- What Ms. Teschow paid to take a taxi from home to school in the morning, with all her workshop supplies - $32.49
- Taxi from school to the Oakville train station - $45.00
- Lunch enroute (could have been saved if I had stayed home in the morning; could have made myself a sandwich before going to the train station in Toronto) - $15.82
- Train ticket from Toronto Union to London - $95
- Ticket from Oakville to London - $74.58
BONUS QUESTION #1:
When Ms. Teschow looked online for the information, she discovered that in fact it was NOT $25, but 25% of the original fee that is supposed to be charged for a change in booking. Does this make a difference to the above problem? Explain your thinking.
BONUS QUESTION #2:
The teacher federation has a discount agreement with the train company of approximately 10%. How does this affect the overall price in the other problem(s)?
Happy calculating! :-)
RSS Feed