
Word Problem
GOING SKIING. LEON DROVE 270 MILES TO THE LODGE IN THE SAME TIME AS PAT DROVE 330 MILES TO THE LODGE. IF PAT DROVE 10 MILES PER HOUR FASTER THAN LEON, THEN HOW FAST DID EACH OF THEM DRIVE?
I REALLY NEED HELP ON THIS ONE. PLEASE! IF YOU CAN SHOW THE WORK WILL BE GREAT I THINK I WILL UNDERSTAND IT BETTER THAN JUST SEEING THE ANSWER. tHINKS

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.