A plane can fly 345 mph in still air. It can fly 200 miles downwind in the same time amount it flies 145 miles upwind, find velocity of wind?
200/(345+w) = 145/(345-w) solve for w mph
Alex has the proper method. But you can reason it out thus: The plane flys at 345 mph through the air. If the plane flys in one direction and an identical plane flys in the opposite direction, they will separate at twice 345mph. Regardless of wind direction or speed. After 0.5 hours they will be 345 miles apart. Which is what we have in the question, 200 + 145 = 345. The still air distance in 0.5 hours is 345/2 = 172.5 miles So in 0.5 hours, the downwind plane has gone an extra 200 - 172.5 = 27.5 miles similarly the upwind plane is short by 172.5 - 145 = 27.5 miles So in each case the plane has drifted 27.5 miles downwind in 0.5 hours. Then the wind speed is 2 x 27.5 = 55 mph
Distance = rate x time 200 = (365+w)t 200 = 365t +wt 145 = (365-w)t 145 = 365t -wt 345 = 730t t = 345/730 w = 58.188