When you’re stuck sitting in traffic, sometimes the line of cars looks like it goes on forever. It doesn’t, of course, but it got our fan Cecilia H. thinking: how many cars could you line up end to end from Los Angeles to New York? Well, there are two answers to this. You could just draw the shortest line from LA to New York — “as the crow flies” — and see how many 16-foot midsize cars would fit. Turns out the cities are 2,448 miles apart. But cars can’t drive that straight line — they can’t just plow through houses and bushes and telephone poles! Cars have to stay on the road, and roads usually don’t run neatly from one place to another. So the driving distance comes to much more, at 2,789 miles. Then we figure out how many cars fit in 1 mile, and then multiply to see how many we can fit across the country. As you’ll see here, that’s a lot of gas tanks to fill!
Wee ones: If you see a blue car, then a red car, then silver, then blue, then red, then silver…what color car comes next?
Little kids: If your car is 1 foot longer than our 16-foot guess, how long is your car? Bonus: If you lined up 4 10-foot Smart Cars instead, how far would they stretch?
Big kids: If you could drive 100 miles an hour nonstop like a maniac, could you get from New York to LA in just 1 day? Bonus: How many 16-foot cars fit in 1 mile, which is 5,280 feet? (Hint if needed: One way to divide by 16 is to cut in half 4 times in a row!)
The sky’s the limit: If you round off to 700 slightly shorter cars per mile, about how many cars can fit from New York to LA, in hundreds of thousands of cars?
Wee ones: A blue car.
Little kids: 17 feet. Bonus: 40 feet.
Big kids: No, since you could drive just 2,400 miles — less than even the crow. Bonus: 330 cars.
The sky’s the limit: If you want your answer in hundreds of thousands, and you’re already multiplying a number (cars) in the hundreds, you can round the other number (miles) to the nearest thousand. That gives us 3,000 miles x 700 cars per mile. Another way to multiply that is 3 x 1000 x 7 x 100, which is 3 x 7 x 100,000 (one hundred thousand). That comes to 2,100,000 cars (which is the same as 21 hundred thousand)!
Laura Bilodeau Overdeck is founder and president of Bedtime Math Foundation. Her goal is to make math as playful for kids as it was for her when she was a child. Her mom had Laura baking before she could walk, and her dad had her using power tools at a very unsafe age, measuring lengths, widths and angles in the process. Armed with this early love of numbers, Laura went on to get a BA in astrophysics from Princeton University, and an MBA from the Wharton School of Business; she continues to star-gaze today. Laura’s other interests include her three lively children, chocolate, extreme vehicles, and Lego Mindstorms.