Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r 

Let r=Dave's speed 

Then r+9=Kent's speed 

Amount of time that Kent drives=472/(r+9) 

Amount of time that Dave drives=400/r 

Now we are told that the above two times are equal, so: 

472/(r+9)=400/r multiply each side by r(r+9) (or cross-multiply) 

472r=400(r+9) 

472r=400r+3600 subtract 400r from each side 

72r=3600 divide both sides by 10

r=50 mph--------------------------Dave's speed 

r+9=50+9=59 mph-----------------------Kent's speed