Plane a flies at a constant speed from new york to los angeles along a route which is 2000 miles. plane b flies in the opposite direction at a constant speed which is 100 mph faster than plane a. plane b takes off one hour after plane a. they land at the same moment. how far are they from los angeles when they pass?

from los angeles distance plan a = 1111.08 mi

from los angeles distance plan b =  888.92 mi

Explanation:

given data

new york to los angeles distance = 2000 miles

Plane b speed = 100 mph faster than plane a

Plane b takes off  time = 1 hour after plane a

to find out

How far are they from los angeles when they pass

solution

we consider speed of plan a is = x mph

so speed of plan b will be = x + 100 mph

and we know plan b take here 1 hour less time than plan a so it mean time is distance divide speed i.e

solve it we get x = 400 mph

it mean here

plan a speed is 400 mph

and plan b speed is 500 mph

and

now we consider they meet at time = t hour  after a take off

then plan a travel  = 400 t

and plan b travel = 500 ( t - 1 )

add both distance that is equal to 2000 mi

so 400 t + 500 ( t -1 ) = 2000

400 t + 500 ( t -1 ) = 2000

400 t + 500 ( t-1) = 2000

solve we get

t = 2.777

so total distance travel plan a = 400 × 2.777 = 1111.08 mi

total distance travel plan b = 2000 - 1111.08

total distance travel plan b = 888.92 mi

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day