A plane flying with the wind went 350 mi in 2 h the return t

A plane flying with the wind went 350 mi in 2 h. the return trip flying against the wind, took 3 h. Find the rate of the plane in calm air and the rate of the wind.

Solution

Let the speed of the plane in calm air be x mph and let the speed of wind be y mph. Therefore 2( x + y) = 350 ...(1) ( distance = time* speed).

Also, 3 (x -y) = 350 ...(2) On multiplying both the sides of equation (1) by 3 and equation 2 by 2, we get, 6x + 6y = 1050... (3) and 6x - 6y = 700...(2) . On adding the equations (3) and (4), we get 6x + 6y + 6x - 6y = 1050 + 700 or, 12x = 1750 so that x = 1750/12 = 145.8333 = 148.83 ( on rounding off to 2 decimal places) On substituting x = 148.33 in the 1st equation, we get 2(148.33 + y) = 350 or, 148.33 + y = 350/2 = 175 so that y = 175- 148.33 = 26.67. We can verify the result by substituting the values of x and y in either of or both the 1st and the 2nd equations. Thus the speed of the plane in calm air is 148.33mph and the speed of the wind is 26.67mph.