Question

at maximum speed , an airplane travels 1680 miles against the wind in 5 hours flying with the wind , the plane can travel the same distance in 4 hours. let x be the maximum speed of the plane and y be the speed pf the wind. what is the speed of the plane with no wind

Answer 1

x = velocity of plane
y = velocity of wind

x - y = 1680/5 = 336 mph .....(1) [ plane flying against the wind]
&
x + y = 1680/4 = 420 mph....(2) [ plane flying with the wind]

Adding (1) and (2) to eliminate y gives

2x = 756
x = 378 mph is the speed of the plane with no wind.

Answer 2

The speed of plane is 378 mph in still air.

Explanation:

Let x be the maximum speed of the plane.

Let y be the speed of the wind.

Distance an airplane travels = 1680 miles against the wind in 5 hours

So, equation becomes,

`(1680)/(5)=x-y` or
`x-y=336` .....(1)

And with the wind, equation becomes,

`(1680)/(4)=x+y` or
`x+y=420` .... (2)

Solving both equations, we get;

`2x=756`

x = 378

And x+y=420

`y=420-378=42`

Hence, the speed of plane is 378 mph and the speed of wind is 42 mph.