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 Ange

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?

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Gianna 3 weeks 2021-10-09T19:35:14+00:00 1 Answer 0

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    2021-10-09T19:36:35+00:00

    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

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