Marcus believes he has the makings of a country music star, so he is flying from Baltimore to Nashville, 700 miles away, to try out his luck. The ride there with the wind takes four hours. A few months later almost broke he heads back, on the same plane and the same wind. The flight then, against the wind, takes five hours. What is the speed of the plane and what is the speed of the wind?
+128474 Let the normal rate of the plane = P
Let the rate of the wind = W
With the wind, the effective rate = (P + W)
Against the wid, the effective rate is (P -W)
And Rate * Time = Distance
So
(P + W) * 4 = 700
(P - W)*5 = 700 simplify
4P + 4W = 700
5P - 5W = 700
Multiply the first equation through by 5 and the second through by 4
20 P - 20W = 3500
20P - 20W = 2800 add these
40P = 6300 divide both sides by 40
P = 157.5 mph
And
4 (157.5) + 4W =700 divide through by 4
157.5 + W = 175 subtract 157.5 from both sides
W = 17.5
