SOLUTION: Ted and Sue leave a resturant at the same time. Ted drives north at 65 mph while Sue drives south. In 1.5 hours, they are 180 miles apart. How fast has Sue been driving?

Two ways.  Without or with algebra.  Here are both ways:

Without algebra.

Their rate of separation is 180 miles per 1.5 hours and 180÷1.5 = 120 mph.
Ted's speed made up 65mph of that 120 mph and so Sue made up the rest of
that 120mph speed of separation or 120mph-65mph or 55 mph.

With algebra.

Let x = Sue's rate.

Make this chart with the rates and their times of 1.5 hrs each:

       Distance        Rate      Time
Ted                     65        1.5
Sue                      x        1.5
-------------------------------------
Total    180

Now fill in the distances using DISTANCE = RATE×TIME

       Distance        Rate      Time
Ted     65(1.5)         65        1.5
Sue     1.5x             x        1.5
-------------------------------------
Total    180

The equation comes from:

                    

                      65(1.5) + 1.5x = 180
                        97.5  + 1.5x = 180
                                1.5x = 82.5
                                   x = 
                                   x = 55 mph

So Sue was driving 55 mph.

Edwin