an aeroplane takes 40 minutes less to fly 3600km with the wind blowing at 30 km/hr than the time it takes to fly against the same wind .Find the actual speed of the aeroplane when there is no wind.

if the speed is s,

3600/(s+30) = 3600/(s-30) - 2/3
s = 570

570

To find the actual speed of the airplane when there is no wind, we need to solve for the airplane's speed with respect to the ground.

Let's assume the actual speed of the airplane is x km/hr.

Against the wind:
Time = Distance/Speed
Time = 3600/(x - 30)

With the wind:
Time = Distance/Speed
Time = 3600/(x + 30)

According to the problem, the airplane takes 40 minutes less time (or 2/3 hours) with the wind compared to against the wind.

Therefore, we can set up the following equation:

3600/(x - 30) - 2/3 = 3600/(x + 30)

To solve for x, we can cross multiply and simplify:

3600(x + 30) - 2/3(x - 30) = 3600(x - 30)

Expanding and simplifying:

3600x + 108000 - (2/3)x + 600 = 3600x - 108000

Combining like terms:

3600x - (2/3)x - 3600x = 108000 + 600 - 108000

- (2/3)x = -108000

Dividing both sides by -2/3:

x = (-108000) / (-2/3)

Simplifying:

x = (-108000) * (-3/2)
x = 162000

Therefore, the actual speed of the airplane when there is no wind is 162000 km/hr.

To find the actual speed of the airplane when there is no wind, we need to set up an equation using the given information.

Let's assume that the airplane's actual speed (when there is no wind) is "s" km/hr.

When the airplane flies with the wind, its effective speed is increased by the wind's speed. So the speed of the airplane with the wind is (s + 30) km/hr.

When the airplane flies against the wind, its effective speed is decreased by the wind's speed. So the speed of the airplane against the wind is (s - 30) km/hr.

We are told that the airplane takes 40 minutes less to fly 3600 km with the wind than it takes to fly the same distance against the wind. Since time is distance divided by speed, we can set up the following equation:

3600 / (s + 30) = 3600 / (s - 30) + 40/60

Let's simplify the equation:

3600 / (s + 30) = 3600 / (s - 30) + 2/3

To get rid of the fractions, we can multiply both sides of the equation by the least common multiple (LCM) of the denominators, which is 3 * (s + 30) * (s - 30):

3600 * 3 * (s - 30) = 3600 * (s + 30) + 2 * (s - 30) * (s + 30)

Simplifying further:

10800 * (s - 30) = 3600 * (s + 30) + 2 * (s^2 - 30^2)

Expand and simplify:

10800s - 324000 = 3600s + 108000 + 2s^2 - 2*900

Rearrange the terms to form a quadratic equation:

2s^2 + 7200s - 432000 = 0

Now we can solve this quadratic equation for "s". We can use the quadratic formula:

s = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 2, b = 7200, and c = -432000. Substituting these values into the formula:

s = (-7200 ± √(7200^2 - 4 * 2 * -432000)) / (2 * 2)

s = (-7200 ± √(51840000 + 3456000)) / 4

s = (-7200 ± √(55392000)) / 4

s = (-7200 ± 7440) / 4

s = (-7200 + 7440) / 4 or s = (-7200 - 7440) / 4

s = 240 / 4 or s = -14640 / 4

s = 60 or s = -3660

Since speed cannot be negative in this context, the actual speed of the airplane when there is no wind is 60 km/hr.