Question

Flying against the wind, an airplane travels 2010 kilometers in 3 hours. Flying with the wind, the same plane travels 10,530 kilometers in 9 hours. What is the rate of the plane in still air and what is the rate of the wind?

Answer 1

it is given that,

the distance travel against wind = 2010

time = 3 hrs

so, the relative speed is = distance/ time = 2010/3 = 670 km/hr

the distance travel with wind is 10,530

time 9 hrs

so,the relative speed is,= 10 530/9 = 1170 km/hr

let a = speed of plane ,

b = speed of wind

so, when plane travel with wind the the relative speed is ,

a + b = 1170

when travel against wind then the relative speed,

a - b = 670

sum the equation

a + b + a - b = 1170 + 670

2a = 1840

a = 920

put a = 920 in equation a + b = 1170

920 + b = 1170

b = 1170 - 920

b = 250

thus, the rate of plane is 920

rate of wind is 250