Question

Two planes A and B can each fly through still air at 550 mph. The distance from Paris to Los Angeles is 5000 miles. Wind blows from Los Angeles towards Paris at a speed of 100 mph. Plane A leaves Paris at noon flying towards Los Angeles. Plane B departs Los Angeles 1 hour later to fly to Paris. How far from Los Angeles are the two planes when they pass each other?

Answer 1

Answer:2688.63 miles

Step-by-step explanation:

Given

Distance between Paris and Los-Angeles $d=5000 miles$

wind blows from Los Angeles to Paris with 100 mph

Velocity of Plane in still Air is $v=550 mph$

Relative velocity of A is $v_a=550-100 =450 mph$  because Plane A is flying opposite to wind

Relative velocity of B is $v_b=550+100=650 mph$

Plane A leaves At 12 noon

distance traveled by Plane A in 1 hr $=450\times 1=450 miles$

Net distance between two Planes is $5000-450=4550 miles$

Suppose they meet after t hr

Distance traveled by Plane B in t time $=v_b\times t=650\times t$

distance traveled by Plane A in t hr is $=v_a\times t=450 t$

Total distance is 4550 miles

$4550=650t+450t$

$t=\frac{4550}{1100}$

$t=4.13 hr$

Distance traveled by B is $=650\times 4.136=2688.63 miles$

i.e. they meet at a distance of 2688.63 miles from Los Angeles