If you are flying to a city 400 miles away, what will be the difference in flight times between flying into a 40-mph headwind and flying with a 40-mph tailwind if the plane's maximum speed with no wind is 160 mph?

Distance = rate * time

400 = (160-40) * time

400 = (160+40) * time

Calculate times and compare.

To calculate the difference in flight times between flying into a 40-mph headwind and flying with a 40-mph tailwind, you need to determine the actual ground speed of the plane in both scenarios.

Case 1: Flying into a 40-mph headwind
In this scenario, the plane is flying against a headwind of 40 mph. The effective ground speed of the plane will be reduced by the speed of the headwind. To calculate the ground speed, subtract the headwind speed from the maximum speed of the plane:
Ground Speed = Maximum Speed - Headwind Speed
Ground Speed = 160 mph - 40 mph
Ground Speed = 120 mph

Case 2: Flying with a 40-mph tailwind
In this scenario, the plane is flying with a tailwind of 40 mph. The tailwind adds to the effective ground speed of the plane. To calculate the ground speed, add the tailwind speed to the maximum speed of the plane:
Ground Speed = Maximum Speed + Tailwind Speed
Ground Speed = 160 mph + 40 mph
Ground Speed = 200 mph

To find the difference in flight times for the two scenarios, divide the total distance (400 miles) by the ground speeds for each case:

Case 1: Flying into a headwind
Flight Time = Distance / Ground Speed
Flight Time = 400 miles / 120 mph
Flight Time = 3.33 hours

Case 2: Flying with a tailwind
Flight Time = Distance / Ground Speed
Flight Time = 400 miles / 200 mph
Flight Time = 2 hours

The difference in flight times between flying into a 40-mph headwind and flying with a 40-mph tailwind is approximately 1.33 hours.

To determine the difference in flight times between flying into a 40-mph headwind and flying with a 40-mph tailwind, we need to consider the effective ground speed.

When flying into a headwind, the ground speed is reduced. The effective ground speed is the plane's maximum speed minus the headwind speed. In this case, the effective ground speed would be 160 mph - 40 mph = 120 mph.

When flying with a tailwind, the ground speed is increased. The effective ground speed is the plane's maximum speed plus the tailwind speed. In this case, the effective ground speed would be 160 mph + 40 mph = 200 mph.

To determine the flight time, we can divide the distance by the ground speed. For flying into a headwind, the flight time would be 400 miles / 120 mph = 3.33 hours (or 3 hours and 20 minutes). For flying with a tailwind, the flight time would be 400 miles / 200 mph = 2 hours.

The difference in flight times between flying into a 40-mph headwind and flying with a 40-mph tailwind would be 3 hours and 20 minutes - 2 hours = 1 hour and 20 minutes.