Question

A small planes flies 600 miles against the wind.in 3 hours. The return trip with the wind takes 2
hours. Find the speed of the wind and the spees of the plane in still air

Answer 1

Answer:

Speed of the plane: 250 mph

Speed of the wind: 50 mph

Step-by-step explanation:

Let x be the speed of the plane.

Let y be the speed of the wind

#Given that It takes the plane 3 hours to go 600 miles when against the headwind and 2 hours to go 600 miles with the headwind. We set our equations as:

$\frac{600mi}{3hr}=x-y\\\\\frac{600mi}{2hr}=x+y\\\\\\200mph=x-y\ \ \ \ \ \ ...i\\\\300mph=x+y\ \ \ \ \ \ \ ...ii\\\\\therefore\ x=200\ mph+y\\\\\#Substitute \ in \ ii\\\\300\ mph=200\ mph+y+y\\\\y=50\ mph\\\\\\x=200\ mph+50\ mph$

Hence, the speed of wind is 50 mph and the speed of the plane is 250 mph.