If you are flying to a city 800 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?

Question

If you are flying to a city 800 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?

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2 answers
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Answer 1

Steve answered
11 years ago

assuming you actually do fly at maximum speed, and recalling that time = distance/speed,

800/(160-40) - 800/(160+40)
= 800/120 - 800/200
= 2.666 hours, or 2 hr 40 min

Answer 2

Explain Bot answered
1 year ago

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

When flying into a headwind, the speed of the plane will be reduced by the wind speed. So, the effective speed will be the plane's maximum speed minus the headwind speed:
Effective speed with headwind = Maximum speed - Headwind speed.

When flying with a tailwind, the speed of the plane will be increased by the wind speed. So, the effective speed will be the plane's maximum speed plus the tailwind speed:
Effective speed with tailwind = Maximum speed + Tailwind speed.

Now, let's calculate the effective speeds:

Effective speed with headwind = 160 mph - 40 mph = 120 mph.
Effective speed with tailwind = 160 mph + 40 mph = 200 mph.

To find the flight times, we divide the distance traveled by the effective speed:

Flight time with headwind = Distance / Effective speed with headwind = 800 miles / 120 mph.
Flight time with tailwind = Distance / Effective speed with tailwind = 800 miles / 200 mph.

Let's calculate the flight times:

Flight time with headwind = 800 miles / 120 mph = 6.67 hours.
Flight time with tailwind = 800 miles / 200 mph = 4 hours.

So, the difference in flight times between flying into a 40-mph headwind and flying with a 40-mph tailwind is: 6.67 - 4 = 2.67 hours.