First note that 24 minutes is 0.4 hour.


Next, we know that the distance from home to Nashville doesn't change, so
if the speed you generally travel is r, and we know that , we can say
that .

We also know that 10 km/hr faster gets us there 0.4 hour sooner, so




 and
 => 


Therefore 


Put everything on the left:



Find the LCD.  Factors are t, (t-0.4), and 1.  So the LCD is t(t-0.4).
Don't bother to multiply it out.  That won't help at this point.


Convert the three fractions to have the LCD:



Simplify the numerator




Since  if and only if  and , we only have to
solve for  and exclude any roots that make 
equal zero because you can't divide by zero.


I'll let you handle the work of solving the quadratic, but suffice it to say
that the roots are 3.4 and -3.  Since we are solving for time, -3 can be
excluded.  As much as we would like to be able to turn back the clock, negative
time just doesn't make much sense.


Knowing that the normal time it takes to get there is 3.4 hours, you can easily
calculate your normal rate,   So your normal rate is 75 km/hr.

Just under 47 mph -- slowpoke!