An airplane can fly 625 miles with the wind in the same amount of time as it can fly 425 miles against the wind. If the wind speed is 50 mph, find the speed of the plane in still air. (Round your answer to the nearest whole number.)
R=rate
d=distance
t=time
c=current
d=(R+C)(t)
625=(R+50)(t)
425+(R-50)(t)
625/(R+50)=t
425/(R-50)=t
equate these two.
625/(R+50)=425/(R-50)
cross multiply
625R-31250=425R+21250
625R-425R=21250+31250
200R=52500
R=262.5
R=263 mi/hr.
check:
625=(263+50)t
t=2hrs.
425=(263-50)t
t=2hrs.
Ergo, the rate of plane in still air is 263 mi/hr.
To solve this problem, we can use the concept of relative speed.
Let's assume the speed of the airplane in still air is "x" mph.
When the airplane is flying with the wind, its effective speed will be the sum of the airplane's speed in still air (x mph) and the wind speed (50 mph). So, the effective speed is (x + 50) mph.
Similarly, when the airplane is flying against the wind, its effective speed will be the difference between the airplane's speed in still air (x mph) and the wind speed (50 mph). So, the effective speed is (x - 50) mph.
Now, let's consider the time it takes for the airplane to travel a certain distance when flying with and against the wind.
When flying with the wind, the time taken to travel a distance of 625 miles is given by:
Time = Distance / Speed
625 / (x + 50)
When flying against the wind, the time taken to travel a distance of 425 miles is given by:
Time = Distance / Speed
425 / (x - 50)
According to the problem, these times are equal, so we can set up an equation:
625 / (x + 50) = 425 / (x - 50)
To solve this equation, we can cross-multiply and simplify:
625(x - 50) = 425(x + 50)
625x - 31250 = 425x + 21250
625x - 425x = 21250 + 31250
200x = 52500
x = 52500 / 200
x = 262.5
So, the speed of the plane in still air is approximately 262.5 mph.