A plane flies 460 miles with the wind and 310 miles against the wind in the same length of time. If the speed of the wind is 30 mph, what is the speed of the plane in calm air?
speed of plane in calm air --- x mph
time to go 460 miles with the wind = 460/(x+30)
time to go 310 miles against the wind = 310/(x-30)
they are equal, so
460/(x+30) = 310/(x-30)
460(x-30) = 310(x+30)
460x - 13800 = 210x + 9300
150x = 23100
x = 154
the speed of the plane is 154 mph
check:
speed with the wind = 184
time of trip against wind = 460/184 = 2.5 hours
speed against wind = 124 mph
time of trip against wind = 310/124 = 2.5 hours.
My answer is correct.
To find the speed of the plane in calm air, we can use the formula:
Speed of the plane in calm air = (Speed of the plane with the wind + Speed of the plane against the wind) / 2
Let's denote the speed of the plane in calm air as "x".
The speed of the plane with the wind is the speed of the plane in calm air plus the speed of the wind, so it is (x + 30) mph.
The speed of the plane against the wind is the speed of the plane in calm air minus the speed of the wind, so it is (x - 30) mph.
We are given that the plane flies 460 miles with the wind and 310 miles against the wind in the same length of time.
Using the formula time = distance / speed, we can set up the following equation:
460 / (x + 30) = 310 / (x - 30)
To solve this equation, we can cross-multiply:
460(x - 30) = 310(x + 30)
Now we can simplify and solve for x:
460x - 13800 = 310x + 9300
150x = 23100
x = 154
Therefore, the speed of the plane in calm air is 154 mph.