19.Rose drove her car from her home to the 
province and back, a total distance of 120km. Her 
average speed returning was 3kph slower than her 
average speed going to the province. If her total 
driving time was 9 hours, what was her average speed 
in going to the province? thanks a lot tutorz!!

Rose drove very slowly to have taken 9 hours to travel 
only 120km. I will assume the traffic was extremely 
heavy both ways.

The words "a total distance of 120km" are ambiguous.  Is 
it 60km going and 60km returning for a total of 120km?  
Or is the total distance between her home and the province 
120km?  Either way she is still driving very slowly.
I will assume she is driving the slowest and the distance
between her home and the province is 60km.

Make this chart:

             DISTANCE    RATE      TIME
Going                                      
Returning                                    

Fill in the two distances, which are both 60:

             DISTANCE    RATE      TIME
Going          60                       
Returning      60                           

Since the question is

>>...what was her average speed in going to the province...<<

We will let x represent her speed going, so we fill in x for 
the rate going:

             DISTANCE    RATE      TIME
Going          60          x             
Returning      60                                  


>>...Her average speed returning was 3kph slower...<<

3kph slower than x kph is x-3 kph. So we fill that in for the 
rate returning:


             DISTANCE    RATE      TIME
               60          x                               
Returning      60         x-3              

Now we use the fact that TIME = DISTANCE/RATE to fill in the 
times:

             DISTANCE    RATE      TIME
Going          60          x       60/x
Returning      60         x-3     60/(x-3)

To find the equation we use this:

>>...her total driving time was 9 hours...<<

We add the two TIME's and put that equal to 9

60/x + 60/(x-3) = 9

Can you solve that by first multiplying through by 
LCD = x(x-3) ? If not post again.

You will get two answers: x = 16 and x = 4/3

We must discard the 4/3, since that would cause her
rate returning to be negative.  So the answer is
a very slow 16 kph.

If we assume it was 120km from her home to the
province the equation is not factorable and the
answer is 28.251 kph, which is still very slow.

Edwin