An airplane flying with a wind of 30 km/hr takes 40 minutes less to fly 3600 km than it would have taken without the wind. Find the plane's speed in still air.

Question

24-05-2025
Physics

High School

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An airplane flying with a wind of 30 km/hr takes 40 minutes less to fly 3600 km than it would have taken without the wind. Find the plane's speed in still air.

Answer :

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shellshiyaira shellshiyaira · Answer 1 · 2024-05-14T17:22:16-04:00

The plane's speed in still air is 387.5 Km/hr.

Let's denote the speed of the airplane in still air as v km/hr.

When the airplane is flying with the wind, its effective speed is the sum of its speed in still air and the speed of the wind. So, the effective speed is v+30 km/hr.

Given that the airplane takes 40 minutes less time to fly 3600 km with the wind than it would take without the wind, we can set up the following equation based on the time difference:

Time taken with wind−Time taken without wind= 40/60

First, let's calculate the time taken to fly 3600 km with the wind and without the wind.

With the wind:

Time taken = Distance / Speed [tex]= 3600/v+30[/tex] hours

Without the wind:

Time taken = Distance / Speed [tex]= 3600/v[/tex] hours

We may now construct the equation:

[tex]3600/v+30 - 3600/v = 40/60[/tex]

To simplify, let's convert 40 minutes to hours: [tex]40/60 = 2/3[/tex] hours.

Now, our equation becomes: [tex]3600/v+30- 3600/v = 2/3[/tex]

â€‹To solve this equation, we'll first find a common denominator:

[tex]-108000/v(v+30) = 2/3[/tex]

Now, cross multiply:

[tex]-108000 × 3 = 2v(v+30)\\-324000 =2v^2 + 60v[/tex]

Now, let's rearrange the equation into a quadratic equation form:

[tex]2v^2+60v-324000=0[/tex]

We have two possible solutions:

[tex]v 1 = -60+1610/4 = 1550/4 =387.5\\v2 = -60-1610/4 = -1670/4 =-417.5[/tex]

We exclude the negative solution because speed cannot be negative.

So, the speed of the airplane in still air is [tex]v=387.5 km/hr[/tex].

Complete Question:

An airplane flying with a wind of 30 km/hr takes 40 minutes less of fly 3600 km, than what it would have taken to fly the same wind. Find the plane's speed in still air.