Question

2. A plane has airspeed of 300km/hr. It flies directly into a head wind for 48 min and returns along the same route in 42 min. What is the wind speed in km/hr?

Answer 1

To determine the wind speed, we can use the concept of relative velocity. Let's assume that the wind speed is represented by 'v' km/hr.

When the plane is flying into the headwind, its effective speed (airspeed - wind speed) is reduced. Therefore, the time taken to cover a certain distance increases. On the return journey, the wind is now assisting the plane, so its effective speed (airspeed + wind speed) is increased, resulting in a decrease in travel time.

Let's calculate the distances covered during the two legs of the journey first:

Distance = Speed × Time

For the first leg (against the wind): Distance = 300 km/hr × (48/60) hr Distance = 240 km

For the return leg (with the wind): Distance = 300 km/hr × (42/60) hr Distance = 210 km

Now, using the concept of relative velocity:

When flying against the wind: Effective speed = Airspeed - Wind speed 240 km = (300 km/hr - v km/hr) × (48/60) hr

Simplifying the equation: 240 = (5/6) × (300 - v)

When flying with the wind: Effective speed = Airspeed + Wind speed 210 km = (300 km/hr + v km/hr) × (42/60) hr

Simplifying the equation: 210 = (7/10) × (300 + v)

Now we have a system of two equations:

1. 240 = (5/6) × (300 - v)
2. 210 = (7/10) × (300 + v)

We can solve this system of equations to find the value of 'v,' which represents the wind speed.

Multiplying both sides of equation 1 by 6/5: 6/5 × 240 = 300 - v 288 = 300 - v v = 300 - 288 v = 12 km/hr

Therefore, the wind speed is 12 km/hr.