Distance/speed/time?

[TicTac1982]

Hi, ive got my ctc coming up, just revising my long division etc etc and just came across a question that i cant get round my head to answer! its as follows:

aircraft a sets off from airport a at 10am and flies towards airport b with a flying speed of 100kts.
aircraft b sets off from airport b at 10am and flies towards airport a with a flying speed of 150kts.

airports a and b are 300miles apart

at what time do the aircraft meet each other?

Is this a simple distance/speed/time answer, im sure its easy, but havent done this kind of maths for years! If anyone could give me a helping hand id appreciate it!

thanks! :ok: :E

[Genghis the Engineer]

Bit of high school algebra will do it.

If we assume that t=time in minutes, s=distance in nautical miles.

At t=0 (actually 10am), Aircraft A is at distance 0, and aircraft B is at distance 300 (the other airfield).

So, position of A is (100/60)*t
And position of B is 300 - (150/60)*t

When they pass, the position is the same (obviously), so

(100/60)*t=300-(150/60)*t

Re-arrange that, and you get:-

( (100/60) + (150/60) ) * t = 300

Divide through by ( (100/60) + (150/60) ) and you get

t = 300 / ( (100/60) + (150/60) )

Which comes out at 72 minutes by my calculator.

So, they'll pass each other at 11:12.

And if you want the position, just use aircraft A: (100/60)*72 = 120nm. So they meet 120Nm from airport A.

To double check, put aircraft B's equation in: 300 - (150/60)*72 = 120, same answer.

G

[nosewheelfirst]

They have a combined speed of 250kts.
The distance they are travelling is 300nm

time=300/250
simplifies to 6/5 which is 1 1/5

so 1hr and 12mins

same answer

am i right in going along those lines as you are expected to do the calculation in your head without a calculator.

[TicTac1982]

Thankyou!

As far as i know, calculators are not allowed, gonna have to use my brain! :8

:ok: :ok:

[Blinkz]

does anyone know of what other types of maths questions get asked? some examples would be nice :ok:

[Tinstaafl]

There's nothing pointless about being able to find the expected crossing time &/or position of a reciprocal aircraft.