Algebra 2
posted by Anonymous .
The point of no return for an airplane, flying over water from point A on land to point B on land, is that distance into the trip for which it takes just as much time to go on to B as it does to return to A. The distance from San Francisco to Honolulu is 2387 miles. A plane leaves San Francisco at a speed, in still air, of 400 mi/h. There is a 60 mi/h tail wind.
a. Find the point of no return.
b. After traveling 1042 miles, the pilot of the plane determines that it is necessary to make an emergency landing. Would it require less time to continue to Honolulu or to return to San Francisco?

I assume the point of no return over water is the same as over land :)
At x miles out, the time to Honolulu is (2387x)/(400+60) and the time to go back to SF is x/(40060)
(2387x)/460 = x/340
811580  340x = 460x
800x = 811580
x = 1014 miles from SF
at 1042 miles, it is obviously quicker to fly on to Honolulu, since it's past the PNR.