plane a is 40 mi south and 100 mi east of plane b. plane a is flying 2mi west for every mile it flies north, while plane b is flying 3 mi east for every mile it flies south. which plane must fly farther
which plane must fly farther
to do what?
To determine which plane must fly farther, we need to find the total distance covered by each plane.
Let's start with Plane A:
Plane A is 40 miles south and 100 miles east of Plane B. Since Plane A will fly 2 miles west for every mile it flies north, we need to calculate the northward distance first.
To fly 40 miles south, Plane A will need to fly 40/2 = 20 miles north.
Now, to find the east-west distance traveled by Plane A, we can multiply the northward distance by the ratio of 2 miles west for every mile north.
20 miles north * 2 miles west/mile north = 40 miles west.
The total distance traveled by Plane A is then:
Distance traveled north + Distance traveled west = 20 miles + 40 miles = 60 miles.
Now let's calculate the total distance for Plane B:
Plane B is flying 3 miles east for every mile it flies south. Since Plane A is 40 miles south of Plane B, Plane B needs to fly 40/3 = 13.33 miles south.
To find the east-west distance traveled by Plane B, we can multiply the southward distance by the ratio of 3 miles east for every mile south.
13.33 miles south * 3 miles east/mile south ≈ 39.99 miles east.
The total distance traveled by Plane B is then:
Distance traveled south + Distance traveled east = 13.33 miles + 39.99 miles ≈ 53.32 miles.
Comparing the total distances traveled by both planes:
Plane A traveled 60 miles, while Plane B traveled approximately 53.32 miles.
Therefore, Plane A must fly farther than Plane B.