Final answer:
To model the situation, we can set up the inequality t + d/(x+5) >= d/x >= 12, where t is the time taken to ride uphill, d is the distance to work, and x is the speed uphill.
Step-by-step explanation:
To model the situation, we can start by setting up an equation for the average speed to and from work. Let's say the distance to work is d miles and the time taken to ride uphill is t hours. Since the speed uphill is at least x mph, the time taken to ride uphill is d/x. The time taken to ride downhill is d/(x+5) since the speed downhill is 5 mph faster. The total time taken for the round trip is t + d/(x+5) = t + d/x. We can then set up the inequality t + d/(x+5) d/x >= 12 to model the situation.