MAM Day 29: Are we there yet?

We've covered math on the T, and math on foot, but math in a car is one of the obvious places where you'll find math. The speedometer is a great start, it's measuring speed in miles per hour. We can use the speedometer and road signs to know how much further we've got to go. If we've been traveling at roughly 70 miles/hour or MPH, and we're 200 miles away from our destination, we should get there in roughly 3 more hours. Easy right?


What I've always wondered is why speedometers go so high, typical highway speeds don't go much higher than 75 mph.
The other big math process we use for cars is determining gas mileage. Gas mileage is how many miles your car can run per gallon of gas. Calculating gas mileage requires that you know how many gallons your car's gas tank holds, and also keeping track of the odometer. The odometer tracks how many miles your car has traveled in total. Newer cars have multiple odometers that can also track the miles on a single trip, very handy for tracking your gas mileage.


The odometers are the counters in the middle.
So if you wrote down the miles off the odometer when you fill up, and then write down the miles at your next fill up (your car should be as empty as possible to track accurate mileage). Find the difference in miles and you have the total miles traveled on that tank of gas. Divide the total miles by how many gallons of gas your car can hold and you've got gas mileage in miles per gallon. Here's an exercise for kids to calculate gas mileage.

Obviously, the higher your gas mileage, the better. Cars typically get better gas mileage on the highway because they aren't wasting gas for starting and stopping. Heavy traffic will cause your gas mileage, your wallet, and your sanity to suffer. My aunt suggested that I keep track of gas mileage to make sure the car is running well. If your gas mileage changes significantly, you'll know something's up and you should take your car to the shop. If you track gas mileage for a few months, you'll get a sense of how long an average tank of gas will last.


I love license plates!
There's tons of numbers on a road trip, from license plates to road signs, billboards to just counting other cars. A great resource for car math ideas.

A video of a mental math game in the car

Although I don't quite understand the sport of car racing (it's incredibly wasteful of gas and I'm not sure how much athleticism is really required for drivers and the spectators) there is a lot of math involved with car racing from car speeds, laps, times in comparison to other cars, and the prep work that's required before a race, tire treads, weight restrictions, and finally the all famous speed of pit crews.

Here's more complex car math including horsepower and torque and tire diameters and gear ratios. Everything else is car lingo I don't understand.

Happy road tripping!



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MAM Day 28: Math on foot

To write this blog today, as a full time pedestrian and part time rider, I am continually interested in rates of walking behind other people, rates of running, juding speeds of cars, etc. So I searched rate of change, math problems that deal with rates of walking or running and found a few great examples.

I found myself longing for my calculus days, when I could understand these pretty complex word problems without a second thought. Working through these following problems, I struggled with the algebra, setting up the problem, and trying my best to remember how calculus makes these problems so much easier.

The rate of change is a foundation of calculus and derivatives. Since I've forgotten most of that and don't particularly want to reteach myself in a few hours, we'll skip over as much of the calculus as possible. Welsh corgis are excellent at doing calculus, maybe they can review calculus with me.


If you'll remember those math problems that state: a train leaves from City A at some time going at x miles per hour and another train leaving from City B leaves at a later time going at a different speed, the word problems tend to ask "When do they meet?" or "Which train gets there first?" These are the problems I'm talking about, distance = rate x time or d=rt. While they're fun to work through, they take up a lot of time and mental concentration to get all the parts right.


If train A and train B are traveling on the same track, shouldn't the question be "When do they crash?"
I worked through this problem using paper and pencil and found that I struggled with the alegbra. Despite my rusty algebra and calculus skills, I found working through the problem to be relaxing. Plus I couldn't stop once I started. The question asks if it's faster to run half a distance then walk the other half, or to run half the time and walk half the time.


This problem was also interesting to read through. I tried to maximize her sponsorship money, but after graphing the equation I realized that she would make the most money if she ran the entire way, but that's not realistic, or what the question was asking. Oh well.

Back to my initial interest in this topic. As a walker in Boston, we've all experienced getting stuck behind someone who is taking their time looking at buildings and the scenery. However, when you're in a rush or trying to catch a bus or T, I severely dislike it when a slowpoke is in front of me on the sidewalk or walking down the stairs. We all walk at different speeds, and I shouldn't blame anyone but myself for being late, but after doing some research, it seems that rates of walking are much more mathematically complex than it would appear.


Effectively navigating the streets of Boston takes a lot of skill.
Walking sometimes requires an optimization analysis, especially if you're running late. Let's say I've got somewhere to be at 6 but leave the office a later than I planned. Should I walk to the nearest T or should I just walk it to the station I would be transferring to later? It ultimately depends on how fast you walk versus how long a wait would be for the T. Other factors like weather also influence people's choices. People cut through grass fields, take smaller roads, use alleys for shortcuts, use the stairs instead of wait for the elevator, etc. Path optimization is anoter part of math on foot.

I also think about judging speeds as a walker. If you're crossing the road when the crosswalk lights haven't said it's ok (jaywalking if you will) you have to properly judge how fast a car is going. You might also have to judge the rate of change in speed if the driver chooses to slow down and let you pass or speed up to try and hit illegal street crossers. I'll try my best to stop jaywalking, but in the meantime, I'll use my rate judgement to stay alive. This goes to show survival skills depend on math.



So today's blog post was brought to you by: rates of change, distance, rate, time, and speed.



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