An airplane can travel 365mph in still air. If it travels 2716 miles with the wind in the same length of time it travels 2394 miles against the wind, what is the speed of the wind?

Answer: the speed of the wind is 365 mph

Step-by-step explanation:

Let x represent the speed of the wind.

An airplane can travel 365mph in still air. If it travels 2716 miles with the wind, it means that its total speed while flying with the wind is (365 + x) mph.

Time = distance/speed

Time spent in flying with the wind is

2716 / (365 + x)

In the same length of time, it travels 2394 miles against the wind. it means that its total speed while flying against the wind is (365 - x) mph.

Time spent in flying against the wind is

2394 / (365 - x)

Since the time is the same, it means that

2716 / (365 + x) = 2394 / (365 - x)

Cross multiplying, it becomes

2716 (365 - x) = 2394 (365 + x)

991340 - 2716x = 873810 + 2394x

2394x + 2716x = 991340 - 873810

5110x = 1865150

x = 1865150/5110

x = 365 mph