Question

A plane flies 450 miles with the wind, and 350 miles against the wind (in the same amount of time). If the wind is blowing at 30 mph, how fast would the plane be going without air helping/hurting?​

Answer 1

Answer: = 240 mph.

Step-by-step explanation:

Let x = speed of the plane.

t= time taken

As per given, we have

$t=\dfrac{450}{x+30}\ \ \ ...(i)\\\\ t=\dfrac{350}{x-30}\ \ \ ...(ii)$    [Time = distance / speed]

From (i) and (ii), we get

$\dfrac{450}{x+30}=\dfrac{350}{x-30}\\\\\Rightarrow\ 450(x-30)=350(x+30)\\\\\Rightarrow\ 450x-13500=350x+10500\\\\\Rightarrow\ 450x-350x=10500+13500\\\\\Rightarrow\ 100x=24000\\\\\Rightarrow\ x=240$

Hence, the speed of the plane = 240 mph.