Math Quiz Simple Answer

Given a mean sea level designated as A,
if a distance of 1,173 ft is required for a
plane to take off when the temperature is
73 degrees F, and 1,356 ft when the temp.
is 86 degrees F, then what distance is required
when the temp. is 79.5 degrees, and given
a different elevation (B) in which a distance of
1,173 ft. is required for takeoff when the temp.
is 70 degrees F, and 1,356 ft.when the temp.
is 80 degrees, then at 75 degrees, what is
the difference in takeoff distance between
the two elevations?


---
Mark

In the first scenerio of elevation A we establish
a relationship of the temperatures, such that the
unknown temperature/distance at 79.5 degrees
is expressed as 6.5/13, because the difference
between 73 degrees and 86 degrees is 13, and
the difference between 73 degrees and 79.5 is
6.5...therefore, 6.5 over 13.

Then obviously, you can do this in your head,
the difference between 1,173 ft. and 1,356 ft is
183. Right?

The only thing missing now is the take-off
distance at 79.5. This is simply...X.

So, by mere logic of interpolation, one can see-

6.5/13 = X/183 right?

Then, 13X = 1189.5

So, X = 91.5

Therefore, 1,173 ft + 91.5 ft = 1264.5 ft at 79.5 degrees

That's the first answer. Now, thru reverse engineering,
we can use trickery and make another simple set of
data which yields the same answer, then apply it to
the landing strip scenerio.

Ok, we want an equation in which the answer comes
out to 91.5 ft again, and uses the same take-off
distance difference of 183.

So...

I establish a temperature relationship between 70
degrees and 80 degrees as...duh, 10. The unknown
distance temperature is now 75, which is simply
expressed as 5 over 10, or 5/10.

Now the numbers are rigged to come out again to
91.5 ft.

So...

5/10 = X/183

and 10X = 915

Therefore, TADA!

X = 91.5 AGAIN. LOL!

And like before, 1,173 + 91.5 = 1,264.5 ft. AGAIN!

Soooooo, same answer for both flight elevations.

---

Or you could have just done the entire thing
in your head the easy way, like I did.

I mean, really...

I just added the two known take-off distances in
my head and divided by 2! LOL!

Ha ha ha ha ha ha ha ha ha ha ha

---
Mark









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