Question

An airplane takes 8 hours to travel a distance of 5824 kilometers against the wind. The return trip takes 7 hours with the wind. What is the rate of the plane in still air and what is the rate of the wind?

Answer 1

Answer:

Speed of plane in still air = 780 km/h

Speed of air = 52 km/hr

Step-by-step explanation:

Let the speed of plane in still air = u km/h

Let the speed of air = v km/h

Against the air, the resultant speed = (u-v) km/hr

With the air, the resultant speed = (u+v) km/hr

Formula for speed is given as:

$Speed = \dfrac{Distance}{Time }$

Given that:

Distance = 5824 km

Time taken against the wind = 8 hours

Speed against the wind:

$u-v = \dfrac{5824}{8} \\\Rightarrow u-v = 728 ...... (1)$

Time taken with the wind = 7 hours

Speed with the wind:

$u+v = \dfrac{5824}{7} \\\Rightarrow u+v = 832 ...... (2)$

Adding (1) and (2):

$2u=1560\\\Rightarrow u = 780\ km/hr$

By equation (1):

$780-v=728\\\Rightarrow v = 52\ km/hr$

Speed of plane in still air = 780 km/h

Speed of air = 52 km/hr