Question 1055875

An airplane flying against the wind travels 500 miles in the same amount of time it would take the same plane to travel 600 miles with the wind. If the wind speed is a constant 50 miles per hour, how fast would the plane travel in still air?
<pre>Let speed of plane in still air be S 
Against the wind, time plane takes to travel 500 miles is: {{{500/(S - 50)}}}
With the wind, time plane takes to travel 600 miles is: {{{600/(S + 50)}}}
Since the times are identical, we get the following TIME equation: {{{500/(S - 50) = 600/(S + 50)}}}
600(S - 50) = 500(S + 50) ------- Cross-multiplying
6(S - 50) = 5(S + 50) ------- Dividing both sides by 100
6S - 300 = 5S + 250
6S - 5S = 250 + 300
S, or speed of plane in still air = {{{highlight_green(matrix(1,2, 550, mph))}}}
<b><u>FYI:</b></u> You DON'T NEED to find time to determine the speed of the plane in still air, regardless of what others might tell you, unless you want to.