I do not know where the 3 hours fit in this word problem?

Question

A plane is traveling between two cities that are 600 miles apart. The plane can travel 200 mies per hour relative to the air, but it will go faster relative to the ground if it is helped by the wind. If the plane completes the trip in 3 hours, how fast was the wind blowing?            Let x+200 ground speed

Let x-200 wind speed                             x+200+x-200=600        Would it be 3(x+200)+x-200=600         

 

 

                   

 

 

 

Answer 1

distance=speed×time, so time=distance/speed=600/200=3 hours. If it takes 3 hrs without the wind for a one-way journey, it should take less time with a tailwind. If it still takes 3 hrs the wind speed is zero. With a headwind it would take more than 3 hours for a one-way journey. If x mph is the speed of the tailwind then the time for the one-way journey is 600/(200+x)<3 when x>0. Example: If the wind speed of a tailwind is 50mph, the time would be 600/250=2.4hrs (2hrs 24mins). If the wind speed is 100mph, the time is 600/300=2hrs. If the headwind speed is 50mph, the time would be 600/150=4hrs and 6hrs with a 100mph headwind.