A car moves from X to Y with a uniform speed vu and returns to Y with a uniform speed vd. The average speed for this round trip is

we defineAverage speed = Distance travelledTime taken = dTLet t1 and t2 be times taken by the car to go from X to Y and then from Y to X respectivelyThen,  t1+t2 = [XYvu]+[XYvd] = XY(vu+vdvuvd)Total distance travelled d = XY +XY = 2XYTherefore, average speed of the car for this round trip isvav = 2XYXY(vu+vdvuvd)   or vav = 2vuvdvu+vd