Hello this is a marvel themed math question. This is a review question and i need help on getting the answer. I really need the answer to this question thank you.

Question

The guardians of the galaxy have to travel in the spaceship Milano from Xander, located on the star map at (-4,-8) to Titan, located at (6,12), to help the avenger stop Thanos. Unfortunately, the fastest route, y=2x, will fly them through an elliptical asteroid field, represented by the equation x^2/16+y^2/4=1. They will travel an average of 0.53 miles per hour, but they must slow down to navigate the asteroid field. While in the field, they will average 0.39 miles per hour. How long will it take them to make the trip?

Answer 1

The line y=2x intercepts the ellipse at (0.97, 1.94) and (-0.97, -1.94). The distance between these two points is about 4.34. The distance between your starting and ending points is 10√3, about 17.32. This means that the distance they travel uninterrupted is 12.98. The time for that portion of the trip is 12.98/0.53 added with the slow portion is 4.34/0.39, which sums to a total time of 35.61 hours.