# Algebra 2

posted by .

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?

• Algebra 2 -

I assume the point of no return over water is the same as over land :-)

At x miles out, the time to Honolulu is (2387-x)/(400+60) and the time to go back to SF is x/(400-60)

(2387-x)/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.

## Similar Questions

1. ### Math

Homing pigeons avoid flying over large bodies of water, preferring to fly around them instead. Assume that a pigeon released from a boat 1 mile from the shore of a lake flies first to point P on the shore and then along the straight …

Ornithologists have determined that some species of birds tend to avoid flights over large bodies of water during daylight hours. It is believed that more energy is required to fly over water than land because air generally rises over …
3. ### Physics

An airplane dropping supplies to northern villages that are isolated by severe blizzards and cannot be reached by land vehicles. The airplane is flying at an altitude of 785m and at a constant horizontal velocity of 53.5 m/s. At what …

It is known that homing pigeons tend to avoid flying over the water in the daytime, perhaps because the downdrafts of air over water make flying difficult. Suppose a homing pigeon is released on an island at point C , which is 3 km …
5. ### Coll Algebra

A grain barge travels on a river from point a to point b unloading and loading again. The barge travels 5mph relative to water. the river flows downstream at a rate of 1mph. if the trip upstream takes 2hrs longer than the trip downstream …
6. ### Math

Flying to the wind, an airplane takes 4 hours to go 960 km. The same plane flying with the wind takes only 3 hours to make the same trip. Find the speed of the plane and the speed of the wind. I wasn't here for the lesson from my teacher …
7. ### geometry

A small airplane takes off from point A and continues to climb upward in a straight line, as shown in the diagram. What is the plane’s distance from point A when it reaches point C
8. ### math

A jet flew at an average speed of 480 mph from Point X to Point Y. Because of head winds, the jet averaged only 440 mph on the return trip, and the return trip took 30 minutes longer. How many hours was the flight from Point Y to Point …
9. ### geometry

A small airplane takes off from point A and continues to climb upward in a straight line, as shown in the diagram. What is the plane’s distance from point A when it reaches point C?
10. ### algebra

A man flies a small airplane from Fargo to Bismarck, North Dakota --- a distance of 180 miles. Because he is flying into a head wind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the …

More Similar Questions