A large commerical jet airplane burns approximately 5gallons of fuel per mile flown plus about 8500 gallons of fuel per Trip to reach cruising altitude. With a useable fuel capacity of 50,000 (there is additional fuel reserved for emergencies) describe the acceptable distance for which an airline could establish a nonstop stop flight

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.