Question 162653
 plane can fly 400 miles downwind in the same amount of time as it can travel 320 miles upwind. If the plane can fly at 360 miles per hour in still air. Find the speed of the wind.
:
Let x = speed of the wind
then
(360-x) speed against the wind
and
(360+x) speed with the wind
:
It says the times are equal for flying 400 mi and 320 mi. Write a time equation
time = {{{distance/speed}}}
:
Time with the wind = time against the wind
{{{400/((360+x))}}} = {{{320/((360-x))}}}
Cross multiply
320(360+x) = 400(360-x)
:
115200 + 320x = 144000 - 400x
:
320x + 400x = 144000 - 114200
:
720x = 28800
x = {{{28800/720}}}
x = 40 mph is the wind
:
:
Check the solution, find out if the times are equal:
Using the wind, the speed with 400, speed against 320
400/400 = 1 hr
320/320 = 1 hr