An airplane can fly downwind a distance of 600 miles in 2 hours. The return trip against the same wind takes 3 hours. Find the speed of the wind. Let w = the speed of the wind Let a = what the speed of the airplane would be if there were no wind 

Then going, flying with the wind, the wind makes the plane go faster, so we add the speed of the wind to what the speed of the plane would be if there were no wind. Therefore, The actual speed going with the wind = a + w Now we use DISTANCE GOING = SPEED GOING × TIME GOING 600 = (a + w)×2 600 = 2(a + w) Divide both sides by 2 300 = a + w Now returning, flying against the wind, the wind makes the plane go slower, so we subtract the speed of the wind from what the speed of the plane would be if there were no wind. Therefore, The actual speed returning against the wind = a - w Now we use DISTANCE RETURNING = SPEED RETURNING × TIME RETURNING 600 = (a - w)×3 600 = 3(a - w) Divide both sides by 3 200 = a - w Now you have two equations in two unknowns: 300 = a + w 200 = a - w Or maybe you would want to write them with the unknowns on the left: a + w = 300 a - w = 200 Solve them and get a = 250 mph and w = 50 mph So the speed of the airplane if there were no wind = 250 mph and the answer to the problem is: The speed of the wind is 50 mph