For this problem, we have to find the maximum distance in miles that the commercial jet plane could travel with the limited capacity amounting to 500,000 gallons. Let's take our solution from two terms: the gallons of fuel consumed per mile traveled, and the gallons of fuel consumed per trip to reach cruising altitude. However, we don't know how many miles there are in a single trip. So technically, we can't solve this problem because of a missing information. But we can do away with this problem by assuming that each trip travels 40 miles. Again, this is just an assumption in order to solve the problem. The equation that we can formulate is:
5x + 8500(x/40) ≤ 50,000
Solving for x,
5x + 212.5x ≤ 50,000
217.5x ≤ 50,000
x ≤ 50,000/217.5
x ≤ 229.89 miles
That means that the plane could travel up to approximately 229 miles before it runs out of fuel.
