An airplane departs from LA and flies to NY every 30 minutes. The trip takes 3 hours and 5 minutes. An airplane takes off from NY at the same time that one takes of from LA and flies to LA at the same speed. How many planes does it pass going in the opposite direction?

The arrival and departure of the airplanes are arranged according to a

schedule that is sequential.

The number of planes it passes going in the opposite direction is 13 planes

Reasons:

The given parameters are;

The frequency of airplane departure = Every 30 minutes

Time it takes to fly from LA to NY = 3 hours 5 minutes

Required;

The number of planes it passes going in opposite direction.

Solution:

As the airplane takes off from NY, we have that the airplane that took off 3

hours earlier from LA is 5 minutes away from the NY.

The airplane are moving in opposite directions, therefore, the relative

speed of the airplane is twice the speed of each airplane.

The time after takeoff at which the airplane from NY pass the first airplane

from LA is 5 minutes ÷ 2 = 2.5 minutes.

The time after which the airplane passes subsequent airplane is two times

faster or half the normal time which is 30 minutes ÷ 2 = 15 minutes, which

gives;

3 hours 5 minutes = 185 minutes

We have an arithmetic progression with first term, a = 2.5, common

difference = 15, and nth term, aₙ = 185, which gives;

Given that the number of planes that the airplane passes are whole

number (discrete) values, we have;

The number of planes it passes going in the opposite direction, n = 13 planes

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We want to see how many planes does a plane that flies from NY to LA sees during the travel.

The answer is 6 planes.

We know that every 30 minutes, an airplane departs from LA to NY.

The travel does take 3 hours and 5 minutes (or 185 minutes in total).

At the same time that an airplane departs from LA to NY, one departs from NY to LA, we want to see how many airplanes it will see.

The number of planes that it will see is given by the number of times that 30 minutes (the interval between planes going from LA to NY) enters in 185 minutes (the total time of the flight).

This gives:

185/30 = 6.2

But we can't have a 0.2 of a plane, so we round the result to the nearest whole number, 6.

This means that on the flight from NY to LA, you can expect to see 6 planes going from LA to NY.

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