The cruising speed of an airplane is 150 mph. You plan to hire the plan for a 3 hour sightseeing trip. You instruct the pilot to fly as far north as she can and still return to the airport at the end of the allotted time. How far north should the pilot fly if the wind is blowing from the north at 30mp.
since time = distance/speed, you have
d/(150-30) + d/(150+30) = 3
Now just solve for d
To determine how far north the pilot should fly, we need to consider the speed of the airplane and the effect of the wind.
The cruising speed of the airplane is given as 150 mph, but we need to account for the wind speed of 30 mph blowing from the north. When flying against the wind, the airplane's ground speed (the speed relative to the ground) will be reduced, and when flying with the wind, the ground speed will be increased.
Let's first calculate the ground speed when flying against the wind:
Ground speed against the wind = Airplane's cruising speed - Wind speed
Ground speed against the wind = 150 mph - 30 mph = 120 mph
Now, let's calculate the ground speed when flying with the wind:
Ground speed with the wind = Airplane's cruising speed + Wind speed
Ground speed with the wind = 150 mph + 30 mph = 180 mph
Since the pilot has 3 hours of allotted time, we can calculate the maximum distance she can travel in each scenario:
Distance against the wind = Ground speed against the wind × Time
Distance against the wind = 120 mph × 3 hours = 360 miles
Distance with the wind = Ground speed with the wind × Time
Distance with the wind = 180 mph × 3 hours = 540 miles
Therefore, the pilot should fly as far north as 360 miles to ensure she can return to the airport within the allotted time.