A plane can fly 500 miles against the wind in the same amount of time that it can fly 775 miles with the wind. If the wind speed is 55mph, find the speed of the plane in still air.
time = distance/speed, so
500/(x-55) = 775/(x+55)
Let's assume the speed of the plane in still air as "p" mph.
When the plane is flying against the wind, its effective speed is reduced by the wind speed. So, the speed of the plane against the wind is (p - 55) mph.
When the plane is flying with the wind, its effective speed is increased by the wind speed. So, the speed of the plane with the wind is (p + 55) mph.
We are given that the plane can fly 500 miles against the wind in the same amount of time that it can fly 775 miles with the wind.
Using the formula Time = Distance/Speed, we can set up the following equation:
500/(p - 55) = 775/(p + 55)
Cross-multiplying, we get:
500(p + 55) = 775(p - 55)
Simplifying the equation, we get:
500p + 27500 = 775p - 42325
Subtracting 500p and adding 42325 to both sides, we get:
69825 = 275p
Dividing both sides by 275, we get:
p = 254.1
Therefore, the speed of the plane in still air is approximately 254.1 mph.
To find the speed of the plane in still air, we can use the formula:
Speed of plane with the wind = (Speed of plane in still air) + (Speed of wind)
Speed of plane against the wind = (Speed of plane in still air) - (Speed of wind)
By substituting the given values, we have:
Speed of plane with the wind = 775 miles
Speed of plane against the wind = 500 miles
Speed of wind = 55 mph
Now we can set up two equations:
775 = (Speed of plane in still air) + 55
500 = (Speed of plane in still air) - 55
Let's solve these equations simultaneously to find the value of the speed of the plane in still air.
From the first equation, we can isolate the Speed of plane in still air:
(Speed of plane in still air) = 775 - 55
= 720 mph
From the second equation, we can also isolate the Speed of plane in still air:
(Speed of plane in still air) = 500 + 55
= 555 mph
Since we have two different values for the speed of the plane in still air, there seems to be an error. Please check the given information again for any mistakes or inconsistencies.