We all have regrets. Perhaps not marrying your college sweetheart, bungee jumping when you were young and agile, traveling around the world before settling down to a 9 to 5 job and raising children, or going up in a small plane so you feel like you’re almost flying it.
One of my biggest regrets was never mastering those train word problems in algebra class that pop up regularly in Marilyn vos Savant’s “Ask Marilyn?” column in Parade Magazine. When I see them, my eyes and brain glaze over.
I could blame my lapse on Teen Talk Barbie, who pronounced to girls around the world decades ago that “math class is tough” sending a message that stuck with many of us. Others regretted that sentence, too, namely, manufacturer Mattel Inc., which removed the chip that utters those words after a women’s group complained.
And now we know that Barbie can do almost anything—and, by extrapolation, so can we. We also know that many women are good at math. I’ve known several from grade school through high school, college, and beyond who excelled and pursued careers in finance, became math or science teachers, physicians, and other math-based professionals.
Sadly, I was among the group that bought into Barbie’s words and found math intimidating–particularly geometry, and never took calculus as a result. In college, I escaped math requirements as an art history and painting major and took only a beginning science class freshman year. Yet, this fear was limiting and led me to drop the possibility of pursuing a career as an architect since I was told I needed to take both calculus and physics to be able to design buildings that would be strong and sturdy.
Maybe, thinking about trains while building a working set for my grandson or seeing pictures of him on his first train ride led me to think back to those puzzling train problems. I decided it’s not too late to learn. My beau, good in math and in a financial field, said he’d break down the formula for me, draw maps of the trains passing, and explain how to solve the equation. Like learning anything on the computer, it’s always better if someone explains it to me while I do the work.
He started with an easy one–maybe, to build my confidence. Suppose Philadelphia and Boston cities are 300 miles apart. If a train leaves Philly traveling at 300 mph how long will it take to get to Boston? One hour, what a piece of cake, chocolate, of course. Not good enough. He insisted I show my work. Because 300 miles or D(istance)/divided by 300 mph or S(peed) = 1 for the T(ime), the answer is one hour.
Like any good teacher, he suggested we check my understanding of the work with a second example. Suppose a train leaves Philly toward Boston traveling at 150 mph how long will it take to get to Boston? Answer this time is two hours because 300 miles or D(istance)/ divided by 150 mph or S(peed) equals 2 hours, the T(ime).
Next, he changed things up a bit to make it more complex and added a second train. Oh boy! If a train leaves Philly traveling at 100 mph (Speed 1) and another train leaves Boston traveling at 50 mph (Speed 2), where will they be when they meet or how much time will have elapsed? If one train is traveling at S1 of 100 mph and another at Speed 2 of 50 mph, how fast are they approaching each other? You add their speeds together, so S1+S2=Speed Total of 150 mph. That’s not so hard.
Next question is tougher, at least for folks like me, and note I didn’t say women! What proportion of the distance will the train leaving Philly travel before they meet? The Speed Total or ST is 150, so the fraction of the Total Distance that Train 1 will cover at the meeting point is S1/ST or 100/150 equals two-thirds or 2/3. And 2/3 times (X) 300 or Total Miles equals 200 miles that Train 1 travels.
The math works the same way if you use Train 2, or 50/150 equals one third or 1/3. And one-third times (X) 300 equals 100 miles that Train 2 travels. Since Train 1 travels 200 miles and is traveling at S1 or 100 mph the time elapsed when they meet is 200/100 or two (2) hours. Check your work. Train 2 is traveling at 50 mph, so Train 2 will cover 100 miles. 100/50 is two (2) hours. Both trains will travel for two hours. But the meeting point will be 2/3ds of the way there because the faster train is traveling 2/3 of the total speed, or 100/150 equals two-thirds or 2/3.
And now for the even more important question–at age 66, do we really care? Yes and no. I can at least say I mastered a new skill. On the other hand, how necessary is it to make these algebraic calculations on paper since we now have at our fingertips an Iphone, GPS, and even that dinosaur Mapquest to track our train trips and print it out if we want. Or simply bag the trains and fly and then you have other problems to handle.
Compared to doing mathematical calculations, I think that bungee jumping might be a snap. I just hold my breath and head downward!