an airplane flew with the wind for 30 minutes and returned the same distance in 45 minutes. If the cruising speed of the airplane was 320 mph what was the speed of the wind ?
speed with wind = 320+x
speed against wind = 320-x
distance with wind = .5(320+x)
distance against = .75(320-x)
but those distances were the same, so ...
.5(320+x) = .75(320-x)
multiply each side by 4 to clear the decimals and solve
Well, if the airplane flew with the wind for 30 minutes and returned the same distance in 45 minutes, then clearly it has mastered the art of time travel! Bravo, airplane! Now, if we assume that the airplane's cruising speed was 320 mph, we can deduce that the speed of the wind was just enough to create a rip in the space-time continuum. Be careful, folks, you never know when a time-traveling airplane might swoop in and steal your watch!
To find the speed of the wind, we can use the formula:
Speed of the airplane + Speed of the wind = Speed of the airplane with the wind
Let's say the speed of the wind is represented by "W".
Given that the airplane flew with the wind for 30 minutes and returned the same distance in 45 minutes, we can set up the following equations:
30 minutes: Speed of the airplane + Speed of the wind = Distance / Time
45 minutes: Speed of the airplane - Speed of the wind = Distance / Time
Since both distances are the same, we can set them equal to each other:
Distance / 30 = Distance / 45
To simplify the equation, we can cross-multiply:
45 * Distance = 30 * Distance
Simplifying further, we get:
45D = 30D
Now, let's solve for the speed of the wind using the given cruising speed of the airplane:
320 + W = Distance / 30 (equation 1)
320 - W = Distance / 45 (equation 2)
From equation 1, we can express the distance (D) in terms of the speed of the airplane and the wind as follows:
D = (320 + W) * 30
Substituting this expression for D in equation 2, we can solve for W:
320 - W = [(320 + W) * 30] / 45
Simplifying the equation:
45(320 - W) = 30(320 + W)
14,400 - 45W = 9,600 + 30W
Combining like terms:
75W = 4,800
Dividing both sides by 75:
W = 4,800 / 75
W = 64
Therefore, the speed of the wind is 64 mph.
To find the speed of the wind, we can use the concept of relative motion.
Let's assume the speed of the wind is "x" mph.
When the airplane is flying with the wind, it effectively moves faster than its cruising speed. So, the speed of the airplane with the wind is the sum of its cruising speed and the speed of the wind, which is (320 + x) mph.
In 30 minutes, the airplane covers a certain distance while flying with the wind.
Distance = Speed × Time
Distance = (320 + x) mph × 0.5 hours
Distance = (320 + x) / 2 miles
Similarly, when the airplane is flying against the wind, it effectively moves slower than its cruising speed. So, the speed of the airplane against the wind is the difference between its cruising speed and the speed of the wind, which is (320 - x) mph.
In 45 minutes, the airplane covers the same distance while flying against the wind.
Distance = Speed × Time
Distance = (320 - x) mph × 0.75 hours
Distance = (320 - x) / 4 miles
Since the airplane covers the same distance in both cases, we can equate the two distances:
(320 + x) / 2 = (320 - x) / 4
Now we can solve this equation to find the value of "x," which represents the speed of the wind.
Cross-multiplying and simplifying, we get:
2(320 + x) = (320 - x)
640 + 2x = 320 - x
Adding "x" to both sides:
3x + 640 = 320
Subtracting 640 from both sides:
3x = -320
Dividing both sides by 3:
x = -320 / 3
Hence, the speed of the wind is -320/3 mph.
Note: Since wind speed is never negative, we can conclude that there is a mistake in the given information or calculations.