Question

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A small plane can fly 350 miles with tailwind in 1 3/4 hour. In the same...

A small plane can fly 350 miles with tailwind in 1 3/4 hour. In the same amount of time, the same plane can travel only 210 miles with a headwind. What is the speed of the plane in still air and the speed of the wind?

Expert Solution

Answer: Speed of plane in still air is 160 miles/hr and speed of wind=40 miles/hr.

Explanation: Let the speed of plane in still air=u miles/hr and speed of wind=v miles/hr. Since, the time taken during the journey is 1 3/4 hrs. i.e.

hrs.

Distance=Velocity*time. ------------------------------------------------ (1)

The velocity of plane with tailwind=(u+v) miles/hr and velocity of plane with a headwind= (u-v) miles/hr.

Since, with tailwind, the distance travelled is 350 miles. So, using eqn 1.

multiplying both sides by (4/7)

------------------------------------------------- (2)

Since, with headwind, the distance travelled is 210 miles. So, using eqn 1.

multiplying both sides by (4/7)

-------------------------------------------------- (3)

Now, adding eqn 2 and eqn 3

dividing by 2 in both sides

----------------------------------------------------- (4)

So, velocity of plane in still air=u=160 miles/hr.

Now, substitute u=160 in eqn 2, we get.

subtracting both sides by 160

-------------------------------------------------- (5)

So, the velocity of wind=v=40 miles/hr.

milcah answered 2 years ago

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