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We’re having a speed contest today between two iconic comic book characters. Can you determine who will win?
The Flash can read 50 pages in an hour. Thor can read 90 pages in an hour. How much faster can Thor read a 300 page book than The Flash?
In a direct physical speed matchup, The Flash will definitely trounce Thor. After all, The Flash has been calculated to travel at ludicrous speed, as fast as13x the speed of light!!! Thor on the other hand, well, the best he can do is hammer speed. The physics of both do not work, but it’s lots of imaginative fun! The Flash was created by being struck by lightning, so, it makes sense for him to run at least the speed of light. Thor on the other hand, is the god of Thunder, and so, perhaps the fastest he can travel is the speed of sound.
What was your answer? Was it 22/3 hours?
If so, then you interpreted “How much faster” as the difference in the time spent reading. The Flash reads 300 pages in 300 pages/50 pages/hour = 6 hours. Thor reads 300 pages/90 pages/hour = 31/3 hours. That means Thor can complete the book 6 – 31/3 = 53/3 – 31/3 = 22/3 hours ahead of The Flash.
Alternatively, we can interpret “How much” as “How many times faster…” . In this case, we’re comparing by ratio. The ratio of Thor’s reading speed to The Flash is 90 pages/hour/50 pages/hour = 9/5 times faster; approximately 2 times faster.
An English major at this juncture may chime in and say, that Thor reads at a rate of 90 – 50 = 40 pages per hour faster than The Flash! Since language is so imprecise, the best protection against an incorrect answer is more language! We encourage our students to show their work and to attach units to numerical values; all of which provides some context and explanation of their interpretation. Then we can have a meaningful conversation rather than saying “right” or “wrong.”
Those two ways of comparing numbers, either as difference or ratio, are useful depending on context. In this question, we find that knowing that Thor reads about twice as fast as Flash is more useful than the difference of 22/3 hours. That’s because we can use the ratio to easily apply it to any number of books and pages. In all cases, Thor reads about twice as fast as Flash!
In the context of a physical race between the characters, the difference in speed is more interesting. The Flash travels at ludicrous speed, let’s say realistically at the speed of light or 670,616,629 miles-per-hour. It will take Flash 0.1 seconds to travel 25,000 miles around the earth. Effectively The Flash can appear in a flash anywhere on earth. Thor in comparison moves ludicrously slow. He travels at the speed of sound or 767 miles-per-hour. We can experience how slow Thor travels because every time we fly in a jet liner (say a Boeing 767), we’re travelling about 6/7 (almost) the speed of sound and it takes forever to get anywhere. The speed of sound is so slow that we can easily track jet planes flying overhead.
So in any race, for example, a one mile race, there is no comparison. The Flash will appear immediately at the finish line, while Thor plods to the finish in 1 mile/767 miles/hour × 60 minutes/hour × 60 seconds/minute = 4.69 seconds ≈ 5 seconds later.
We can use that factoid in real life to measure distance in miles to any observable activity that makes brief intermittent noise, for example lightning. When we see the flash from lightning, count the seconds until we hear the accompanying thunder. For every 5 seconds we count, the lightning is about 1 mile away! 1-second means 1/5 mile (about 1,000 feet) and you’ve probably dove for shelter in a flash!
Contact:
Ruby Yao and Benedict Zoe, Mathnasium of Fort Lee
201-969-6284 (WOW-MATH), [email protected]
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Pictures: https://comicvine.gamespot.com
