Math problems you can solve on the TTC!

We’ve all been there: you’re sitting on the subway, there’s absolutely ZERO service on your phone (but you’re still checking it anyway) and you start to read ads to avoid making contact with just about everyone. And chances are you’re thinking “yeah, well what else could I be doing on public transit? It’s not like I could be doing something totally awesome like MATH, right?” WELL, YES YOU CAN! Here is some awesome and simple Math you can do on the TTC to occupy your mind!


Probability is most likely the math you’ll see most while riding the TTC. Take this little math problem as an example:

There are 100 passengers pushing through the SAME door at once as the subway arrives. There are a total of 3 clean and ‘sittable’ seats remaining of the dozen seats available on the subway car. 2 of the ‘sittable’ seats are beside strangers sitting very widely. If 100% of those 100 passengers are looking for one of those ‘sittable’ seats and 85 of them do not want to sit beside the stranger, what is the probability that you get one that is not beside the stranger and the probability that you get the one that IS beside the stranger?

While you’re figuring out the result to this probability problem, you more than likely will end up standing. But hey! Now you know you can solve simple probability problems on the TTC!

Time Management

Time is SUPER important when you need to get from one place to another. Ensuring you have on-point time management skills will help you make sure you get to where you need to on time! Here’s a super simple time problem we’ve ALL done at least once: 

From the moment that you tap a Presto card, you are granted a 2-hour transfer period. You’re heading downtown to meet up with some friends at a restaurant and want to only pay ONCE for your TTC fares. You figure it will take you 30 minutes on the subway to get downtown, then 5 minutes to walk to the restaurant from the station. You know your one friend will order the soufflé, extending dinner time to 75 minutes. Then you race back to the station which will take you 5 minutes once again. Will you make it back to the station within the 2-hour transfer period? Fact is, it doesn’t really matter since it’s now 11:00pm and the station is closed for “ATC SIGNAL UPGRADES”.

Knowing how to plan your route accordingly, knowing when the next bus comes, knowing how long the subway ride is as well as adding extra time in case of any unforeseen delays will make you a TTC-riding pro!



This one goes out to all the physics-loving people! WE SEE YOU! You can solve some AWESOME simple physics problems while you’re riding the bus! Try this one out:

A bus is cruising at a speed of 38km/h down Yonge Street. A passenger calls out to the driver that his requested stop has been passed. The driver apologises and brings the bus to a halt in a matter of 0.5 seconds. Calculate the acceleration it took to bring the bus to a complete stop.

You can also tie acceleration/deceleration problems back to probability problems! You can calculate the probability that you’ll lose your balance for relying on the little rubber strap things. Like seriously, HOW is that thing supposed to help you keep your balance on a bus?!


Planning your travel budget for the next month while you’re riding on the TTC will help you SO much for when that month rolls around! Here’s a simple budgeting problem you can do:

You’re planning out your budget for the following month and are deciding whether you should load your Presto card with fare or a monthly Metropass. Given your work schedule, you will need to ride 20 times per month BOTH ways to commute. You also estimate that you will need to ride at least 4 times BOTH ways to hang out with your friends. Assuming standard rates are $3.10 per ride and monthly Metropass is a flat $122.45 - which would be the better choice? BUT WAIT! You now factor in that on 25% of your rides, the Presto machines are SHOCKINGLY broken and don’t require you to pay! NOW which option is ideal?

Your wallet will LOVE you for planning out your monthly travel budget ahead of time! You can give yourself a pat on the back too for not hopping turnstiles and ACTUALLY paying your fare! Good on you!