Question

PLEASE HELP I NEED AND ANSWER

Flying against the wind, an airplane travels 5040 kilometers in 6 hours. Flying with the wind, the same plane travels 6000 kilometers in 5 hours. What is the rate of the plane in still air and what is the rate of the wind?

Answer 1

The rate of plane in still air is 1020 kilometers per hour and rate of wind is 180 kilometers per hour.

Explanation:

Given that:

An airplane travels 5040 kilometers in 6 hours against the wind

An airplane travels 6000 kilometers in 5 hours with the wind

Let,

x be the speed of plane in still air

y be the rate of wind

Combined speed against the wind = x - y

Combined speed with the wind = x+y

Speed =
`(Distance)/(Time)`

x-y=
`(5040)/(6) = 840`

x - y = 840 Eqn 1

x + y =
`(6000)/(5) = 1200` Eqn 2

Adding Eqn 1 and 2

x+y+x-y=1200+840

2x=2040

Dividing both sides by 2

`(2x)/(2)=(2040)/(x)\\x=1020`

Putting x=1020 in Eqn 2

1020+y=1200

y=1200-1020

y=180

Hence,

The rate of plane in still air is 1020 kilometers per hour and rate of wind is 180 kilometers per hour.