With a certain tail wind a jet aircraft arrives at its destination, 1,890 miles away, in 3 hours. Flying against the same wind, the plane makes the return trip in 3 3/8 hours. Find the wind speed and the plane's airspeed.
Find the wind speed and the plane's airspeed. : Let s = speed of the plane in still air Let w = speed of the wind then (s-w) = plane speed against the wind and (s+w) = plane speed with the wind : Change 3 3/8 hrs to 3.375 hrs : The trips there and back are equal distance, (1890 mi) write two distance equations dist = time * speed : 3.375(s-w) = 1890 3.0(s + w) = 1890
: It is convenient that we can simplify both these equations: divide the 1st by 3.375 divide the 2nd by 3 resulting in two simple equations that can be used for elimination of w s - w = 560 s + w = 630 ----------------adding eliminates w, find s 2s = 1190 s = s = 595 mph is the plane speed in still air Find w 595 + w = 630 w = 630 - 595 w = 35 mph is the wind spee
