It took a manticore the same amount of time to fly 10 miles with the wind as 5 miles against the wind what is the speed if the wind if the manticore flies 30 mph in still air?
time = distance/speed, so
10/(30+x) = 5/(30-x)
Now just solve for x
10 mph
Well, it seems like that manticore is quite a wind-savvy creature! Let's see if we can unravel this amusing airborne riddle.
If the manticore flies 30 mph in still air, we'll call that its airspeed velocity. Now, when the manticore flies with the wind, it takes the same amount of time to cover 10 miles as it does flying 5 miles against the wind.
To figure out the speed of the wind, let's imagine the manticore flying against the wind. If we subtract the speed of the wind from its airspeed of 30 mph, we get the speed at which it's effectively flying against the wind.
So, let's say the speed of the wind is "w" mph. If the manticore's airspeed is 30 mph and it's flying against the wind, its ground speed would be 30 - w mph.
Now, flying with the wind, its ground speed would be 30 + w mph. And we know that it takes the same amount of time to cover 10 miles at that speed as it does to cover 5 miles flying against the wind.
Since speed equals distance divided by time, we can set up an equation:
10 / (30 + w) = 5 / (30 - w)
Now, let's do some math magic to solve this equation. Cross-multiplying, we get:
10 * (30 - w) = 5 * (30 + w)
Simplifying that, we have:
300 - 10w = 150 + 5w
Combining like terms:
-15w = -150
Dividing both sides by -15:
w = 10
So, the speed of the wind is 10 mph! That manticore is one swift and breezy flyer! Keep an eye out for gusty jokes on your next flight with it!
To find the speed of the wind, we need to determine the difference in time it took the manticore to fly with the wind and against the wind.
Let's start by considering the manticore's speed with the wind. We know the distance it traveled was 10 miles, and it took the same amount of time as flying 5 miles against the wind.
We can calculate the time it took the manticore to fly with the wind using the formula:
Time = Distance / Speed
So, for flying 10 miles with the wind, the time can be calculated as:
Time with wind = (Distance with wind) / (Speed with wind)
= 10 miles / (30 mph + Wind speed)
Next, we can calculate the time it took to fly against the wind. This time will be the same as flying 5 miles, so we can use the formula again:
Time against wind = (Distance against wind) / (Speed against wind)
= 5 miles / (30 mph - Wind speed)
Since we know that the times are equal (from the problem statement), we can write an equation:
Time with wind = Time against wind
Substituting the formulas we derived earlier:
10 / (30 + Wind speed) = 5 / (30 - Wind speed)
To solve for the wind speed, we can cross-multiply and solve for Wind speed:
(10) * (30 - Wind speed) = (5) * (30 + Wind speed)
Simplifying:
300 - 10 * Wind speed = 150 + 5 * Wind speed
Bringing similar terms together:
10 * Wind speed + 5 * Wind speed = 300 - 150
15 * Wind speed = 150
Wind speed = 150 / 15
Wind speed = 10 mph
Therefore, the speed of the wind is 10 mph.