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Math PagesEstimating ETAFun Stuff |
Two-bit mathLast time we learned how to chew out ETEs for aircraft that fly 2 or 3 miles per minute. But, what about all those airplanes that cruise right around 150 knots, or 2.5 miles per minute. Don't you just hate that? Who can divide by 2.5? The answer is - you can. It's so simple your going to kick yourself when you see the trick to this. Forget about airplanes for a minute. Say you go into the 7-11 to get a snack. You drop it on the counter and the clerk says "that's a buck sixty." You reach into your pocket and all you have is a fist full of quarters. How many do you give the clerk? We do this problem so often that we stop thinking of it as a math problem - we just give the guy 7 quarters. For most people we hardly even have to think about it. But what we have really done mathematically is divide 160 by 25 - which is in turn the same as dividing 16 by 2.5. So, here's how a pro pilot does it: If there are 16 miles to go at 150 knots (2.5 miles per minute) just move the decimal and call it $1.60. Then, pay for it in quarters. It will take 7 and you get a bit of change - i.e. it will take just under 7 minutes. Lets do a couple more just to make sure we have the idea. How many minutes to fly 27 miles. That's $2.70 in quarters, or just under 11 minutes. How about 55 miles. That's just over 22 quarters. If your didn't get that last one too easily it's probably because you haven't memorized the four times table. Remember last month when we learned to chew we had to memorize the three times table. And we noted that when we get a job flying a King Air we will need to memorize the four times table. So, since we are going to fly a King Air someday, and besides we have to make change at 7-11, all fiscally responsible people should memorize the following:
Once you have the above 4 times table memorized any distance up to 10 dollars, or 100 miles is easy. For example how long to go 84 miles. That's $8.40 and we know that $8.00 is 32 quarters, so we need an extra two quarters, for a total of 34 minutes. What if the distance is more than 100 miles? Say I have to fly 170 miles at 150 knots. That's $17.00 dollars - I don't have that memorized. What do I do? You could chew it, as we did last week. We say that it will take 40 minutes to go 100 miles, so the extra 70 miles ($7.00 dollars) will take 28 more quarters so the answer is 68 (40 plus 28.) But, there is an easier way to do it, although it's a bit less accurate. If the distance is more than $10 after you have moved the decimal once, just keep moving the decimal and count how many extra times you have to move it. So, for example 170 miles becomes $17 dollars if we move the decimal once, but one extra move makes it $1.70. Now solve the problem as we always do - $1.70 costs 7 quarters. But since we know we moved the decimal one extra time our answer is not 7 but 70 minutes to go 170 miles. In other words add one zero to your answer for each extra decimal you moved. As you can see this is off a bit, because chewing showed the answer is really 68 - but over such a long distance the two minute error is not significant, so I recommend just moving the decimal on any distance until the value is less than $10. Just remember to count the extra times you move the decimal and add that many zeros to your answer.
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