A plane can fly 140 mph in calm air. Flying with the wind, the plane can fly 700 mi in the same amount of time it takes to fly 420 mi against the wind. Whats the rate of the wind?
Let V be the wind speed. The flight time is D/(140+V)with a tail wind and
D/(140-V) with a head wind.
Solve 700/(140+V) = 400/(140-V)
98,000 -700V = 56,000 +400V
1100V = 42,000
V = 38.2 km/h
Thanks
To solve this problem, let's assume that the speed of the wind is represented by "x" mph.
When the plane is flying with the wind, its effective speed is increased by the speed of the wind. So, the speed of the plane flying with the wind is (140 + x) mph.
On the other hand, when the plane is flying against the wind, its effective speed is decreased by the speed of the wind. So, the speed of the plane flying against the wind is (140 - x) mph.
We can use the formula: Speed = Distance / Time
Let's calculate the time it takes to fly 700 miles with the wind:
Time with the wind = 700 / (140 + x)
Now, let's calculate the time it takes to fly 420 miles against the wind:
Time against the wind = 420 / (140 - x)
Given that these times are the same, we can set up an equation:
700 / (140 + x) = 420 / (140 - x)
To solve for "x", we can cross-multiply and simplify:
700(140 - x) = 420(140 + x)
98000 - 700x = 58800 + 420x
Combining like terms:
700x + 420x = 98000 - 58800
1120x = 39200
Dividing both sides by 1120:
x = 39200 / 1120
x = 35
Therefore, the rate of the wind is 35 mph.
To find the rate of the wind, we need to set up an equation based on the information given.
Let's suppose that the rate of the wind is "x" mph.
When flying with the wind, the speed of the plane is increased by the rate of the wind, so the effective speed of the plane is 140 + x mph. In this case, the plane can fly 700 miles.
When flying against the wind, the speed of the plane is decreased by the rate of the wind, so the effective speed of the plane is 140 - x mph. In this case, the plane can fly 420 miles.
Now, we can calculate the time it takes in both scenarios. The time it takes to travel a certain distance is given by the formula: time = distance / speed.
Flying with the wind:
time = distance / speed = 700 / (140 + x)
Flying against the wind:
time = distance / speed = 420 / (140 - x)
According to the problem, the time it takes to fly with the wind is the same as the time it takes to fly against the wind. So we can set up an equation:
700 / (140 + x) = 420 / (140 - x)
To solve this equation, we can cross-multiply:
700 * (140 - x) = 420 * (140 + x)
Simplifying further:
98000 - 700x = 58800 + 420x
Combining like terms:
700x + 420x = 98000 - 58800
1120x = 39200
Now, divide both sides by 1120 to isolate x:
x = 39200 / 1120
x = 35
Therefore, the rate of the wind is 35 mph.