Puzzling question

There's a local (Houston) morning radio show that regularly has a feature called 'You Can't Win' wherein the DJ typically comes up with extremely obscure trivia and tries to stump the listeners. He asks the same questions, day after day, eventually giving hints, until someone gets them, then he comes up with new ones. Currently, he's featuring a question that seems to be a logic or number sequence type problem, rather than trivia and he's very smug when he says it's going to take a long time for anyone to figure it out. Perhaps someone here can help put him in his place.

The question:

A times B equals 270; C times D equals 440; what is F? And, more importantly, why?

That's the whole problem. Some of the incorrect guesses so far have been: 5, 13, 130, 95, 61, 440, 2.5

Today he gave the following hint(s): If you figure out the WHY part, the answer will be obvious. The math is a red herring.

Anyone have any ideas?

The sixth letter in the alphabet?

Maybe it is has something to do with the frequency of musical notes.

When the question was read out, did the DJ say two-seven-zero or two-seventy or two hundred and seventy? or some other form?

Which show is this? Mark and Brian (KLOS, Los Angeles; syndicated to various other cities, but apparently not Houston) ran a feature with the same name and concept. It was discontinued after twenty rounds of five questions each.
http://www.955klos.com/viewentry.asp?ID=183159& PT=markandbrian&FN=Mar... an

(This should be all one line. Cut and paste as needed.)

Might 270 and 440 be highway numbers? Batting averages?

See http://www.thebuzz.com/cantwin.html

I wonder why it says 'Any WHY?' rather than 'And WHY?' Typo or clue?

What was today's clue?

Well, I figure that there is something funny about the missing 'E'. I got to thinking that it is in the '*e*quals.' So than I got to thinking:

Perhaps 'Equals' is 'E quells.'

Quell means 'to yield.'

Also, I was going to ask for the specific wording of the last phrase: 'What is F?' Above it is: 'What does F equal?' This is important if we go along this syllabic track.

Now let's put it all down in syllabic form:

A times BE quells to 70, C times DE quells for 40 FE quells what?

You can further break it down and get:

270 = to seven T

So:

A times BE quells to 7, TC times DE quells for 4 TFE quells what?

Now using these equations, is it possible to solve for F? No, but we can show what F equals in an equation. Perhaps that equation if read phonetically produces some answer. Perhaps this answer has the syllables 'A B C D For T Seven' in it?

Also, on other lines,

Effie quells what? Fe (Faith) quells what?

The station is KTBZ ('The Buzz' in Houston and the DJ is named Jeff McMurray

Here's how it appears on the radio station's webpage:

Question #5: a x b=270. c x d=440 What does f equal? Any WHY?

(The DJ confirmed that the 'Any WHY?' is a typo that should read 'And WHY?'