The question "how fast" shows you that the numerical answers you want is somebody's speed: in fact you want both Pat's and Leon's speeds. Call these P and L mph respectively. You're now told that Pat's speed was 10 mph faster than Leon's, so P = L+10. You're also told that Pat drove 330 miles in the same time Leon drove 270. But Pat would have taken time = distance/speed = 330/P and Leon took time = distance/speed = 270/L (hours): and these are said to be the same, so 330/P = 270/L.
Now we do the algebra. 330/P = 270/L so multiplying up 330L = 270P. Substituting P = L+10 in this, 330L = 270(L+10) = 270L + 2700. So 60L = 2700, and we have L = 2700/60 = 45 and then P = L+10 = 55.
We now check by seeing that Pat drove 330 miles at 55 mph so took 330/55 = 6 hours; and Leon drove 270 miles at 45 mph and took 270/45 = 6 hours.