Logan, the way you have phrased this question makes it a bit hard to follow. I'm going to take the liberty of paraphasing it:
"Catalan drives an average of 1.4 times faster during the first 105 miles of her trip than she does during the second 105 miles."
As we are told, let X represent her speed during the first 105 miles of her trip. She drives more slowly during the second 105 miles. Thus, her speed during the 2nd 105 miles is X/1.4.
Remember: distance = (rate)(time), or time = (distance)(rate)
We need to determine an expression for the time she spends driving. Let T1 be the time required to drive 105 miles at speed X mph and T2 be the time required to drive 105 miles at speed (X/1.4) mph.
What is the total time required to drive these 210 miles?
Total time = (time required to drive 105 miles at X mph) + (time required to drive 105 miles at X/1.4 mph).
This gives you TIME SPENT DRIVING as a function of X, her speed during the first 105 miles of driving.
