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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 in still air. Find the plane's speed in still air.

Answer :

The speed of the airplane in still air is ( 387.5 ) km/hr.this problem given that the airplane takes 40 minutes less time to fly 3600 km with the wind than against it, we can set up the following equation based on the formula:

- Speed of the airplane in still air as ( v ) (in km/hr)

- Time taken by the airplane to fly 3600 km with no wind as ( t ) (in hours)

Given that the wind speed is ( 30 ) km/hr, the effective speed of the airplane when flying with the wind is ( v + 30 ) km/hr, and against the wind is ( v - 30 ) km/hr.

Now, according to the problem, the difference in time taken is ( 40 ) minutes, which is equivalent to ( frac{40}{60} = frac{2}{3} ) hours.

So, we can set up the equation:

[ text{Time taken with no wind} - text{Time taken with wind} = frac{2}{3} ]

[ frac{3600}{v} - frac{3600}{v+30} = frac{2}{3} ]

Now, let's solve this equation for ( v ):

[ frac{3600(v+30) - 3600v}{v(v+30)} = frac{2}{3} ]

[ frac{3600v + 108000 - 3600v}{v² + 30v} = frac{2}{3} ]

[ frac{108000}{v² + 30v} = frac{2}{3} ]

[ 3 cdot 108000 = 2(v² + 30v) ]

[ 324000 = 2v² + 60v ]

[ 2v² + 60v - 324000 = 0 ]

Now, let's solve this quadratic equation to find the value of ( v ). We can use the quadratic formula:

[ v = frac{-b pm sqrt{b - 4ac}}{2a} ]

Where:

- ( a = 2 )

- ( b = 60 )

- ( c = -324000 )

[ v = frac{-60 pm sqrt{60² - 4 cdot 2 cdot (-324000)}}{2 cdot 2} ]

[ v = frac{-60 pm sqrt{3600 + 2592000}}{4} ]

[ v = frac{-60 pm sqrt{2595600}}{4} ]

[ v = frac{-60 pm 1610}{4} ]

Now, we'll have two values for ( v ), but we'll only consider the positive one since speed can't be negative:

[ v = frac{-60 + 1610}{4} ] (ignoring the negative root)

[ v = frac{1550}{4} ]

[ v = 387.5 ]

Therefore, the plane's speed in still air as 'x' km/hr, and the time taken to cover 3600 km with the wind as 't' hours. According to the problem, the plane takes 40 minutes less (or 2/3 hours) with the wind. So, the speed of the airplane in still air is ( 387.5 ) km/hr.

Completed question:

an aeroplane 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.

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Rewritten by : Jeany

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