How Far Did the Plane Fly?

Date: 01/23/2003 at 00:56:09
From: Kylee
Subject: How far did the plane fly?

A plane flew 440km/h to its destination. It then flew 500km/h back. If 
the whole trip took 9 hours, how far did the plane fly?

Date: 01/23/2003 at 13:57:50
From: Doctor Edwin
Subject: Re: How far did the plane fly?

Hi, Kylee.

I find two things help when setting up algebra problems like this. 
First, write down every equation you can think of, even if it doesn't 
capture everything you want. Second, don't be afraid to write 
equations that are full of unknowns. For example, we know that the 
plane made two trips and the total time was nine hours:

   Time out + time back = 9 hours

Let's call them t_1 and t_2:

<1>       t_1  +    t_2    =   9h

Not exactly earth-shaking, but it's a start. Now, what IS t_1? How 
much time did the plane take? I take a look around to see if I know 
any formulas involving time in a situation like this and I come up 
with:

<2>      speed = distance/time

Now on the trip out the plane was going 440km/h, so we get (let's use 
d for distance of ONE trip - that is, half the total distance):

<3>               d
           440 = ---
                 t_1

On the trip back, it's going 500km/h:

<4>               d
           500 = ---
                 t_2

Solving <3> and <4> for d, we get:

             d = 440 * t_1
             d = 500* t_2

So:

<5>  440 * t_1 = 500 * t_2

But we also know that t_1 + t_2 = 9 (from equation <1>). Can you solve 
these two equations together?

Write back if you're still stuck on either problem.

- Doctor Edwin, The Math Forum
  http://mathforum.org/dr.math/