Question

An airplane is flying from Dallas, Texas to Pensacola, Florida. Flying at maximum velocity, it encounters strong winds moving at half the speed of the plane in the opposite direction. How long will it take the plane to arrive in Pensacola, relative to the original arrival time?

F. It will take half the time.
G. It will take twice as long.
H. It will take 1.5 times as long.
I. It will take three times as long.

Answer 1

G. It will take twice as long.

Step-by-step explanation:

Let's call
`v` the original speed of the plane and
`d` the distance between Dallas and Pensacola. The time the plane originally takes to complete the flight is

`t=(d)/(v)`

In this problem, we are told that the plane encounters wind moving at half of its speed:
`(v)/(2)`, in the opposite direction. This means that the new speed of the plane is

`v'=v-(v)/(2)=(v)/(2)`

And so, the time the plane takes now to complete the flight is

`t'=(d)/(v/2)=2(d)/(v)=2t`

So, the plane takes twice the time as before.