Question

An airplane travels 6032 kilometers against the wind in 8 hours and 7312 kilometers with the wind in the same amount of time. What is the rate of the plane in
still air and what is the rate of the wind?

Answer 1

Answer:

The rate of plane in still air is 834 km/hr and the rate of wind is 80 km/hr.

Step-by-step explanation:

The airplane travels 6032 km in 8 hours against the wind.

So, $u -v = \frac{6032}{8} = 754$ ........ (1) {Where u is the speed of plane in still air and v is the wind speed}

Again, the airplane travels 7312 km in 8 hours with the wind.

So, $u +v=\frac{7312}{8} =914$ ........ (2)

Now, adding equations (1) and (2) we get,

2u = 1668

⇒ u = 834 km per hour.

So, from equation (1), we get  

v = u - 754 = 834 - 754 = 80 km per hour.

Therefore, the rate of the plane in still air is 834 km/hr and the rate of wind is 80 km/hr. (Answer)