Question

An airplane flying into the wind travels the 1800-mile flying distance between two cities in 3 hours and 36 minutes. On the return flight, the plane took 3 hours to get back. What is the plane speed AND the wind speed? Please solve using algebra.

a) Plane speed = 500 mph, Wind speed = 100 mph
b) Plane speed = 400 mph, Wind speed = 200 mph
c) Plane speed = 600 mph, Wind speed = 100 mph
d) Plane speed = 450 mph, Wind speed = 150 mph

Answer 1

To solve this problem, we can use the concept of relative velocity. By solving two equations simultaneously, we can find the values of the plane speed and wind speed. The correct answer is d) Plane speed = 450 mph, Wind speed = 150 mph.

Step-by-step explanation:

To solve this problem, we can use the concept of relative velocity. Let's assume the speed of the plane (plane speed) is 'p' mph and the speed of the wind (wind speed) is 'w' mph.

Given that the plane took 3 hours and 36 minutes (or 3.6 hours) to travel 1800 miles against the wind:

Plane speed - Wind speed = 1800 / 3.6

p - w = 500

Similarly, for the return flight, the plane took 3 hours:

Plane speed + Wind speed = 1800 / 3

p + w = 600

Now we can solve these two equations simultaneously to find the values of 'p' (plane speed) and 'w' (wind speed).

Solving the equations, we get p = 450 and w = 150. Therefore, the correct answer is d) Plane speed = 450 mph, Wind speed = 150 mph.