Suppose you are flying from Pittsburgh, PA to Los Angeles, CA. The distance between the cities is 2,400 miles and the plane's speed is 450 mi/hr. What is the speed of the wind?
Any help?
Also, the trip is going to take 11 hours.
I got a formula of: 11 = 2400/450+x + 2400/450-x
I got 10.7 with decimals but any other help would be great.
looks good, except that online, due to formatting handicaps, you should use parentheses to remove ambiguity:
11 = 2400/(450+x) + 2400/(450-x)
I was told that the wind speed is 50, but I'm not sure how to get there.
the wind speed is clearly not 50, since
2400/500 + 2400/400 = 10.8, not 11
You have solved for a round trip. The problem didn't say that, but taking 11 hours for one-way means a speed of about 218 mph, too slow.
Something is screwy with this problem.
Solving your equation gives x ≈ 78.335
Right? I got that also. I used an online calc and I got 150 sqrt 33/11 to get x ~= 78.335!
To find the speed of the wind, you need to use the concept of relative motion. The speed of the airplane is given as 450 mph, which is its airspeed. However, the actual ground speed, which takes into account the wind, may be different.
To determine the wind speed, you can use the following formula:
Ground Speed = Airspeed + Wind Speed
In this case, the ground speed is the distance between Pittsburgh and Los Angeles (2,400 miles) divided by the time it takes to travel that distance.
To calculate the time it takes to travel the distance, you can use the formula:
Time = Distance / Speed
Plugging in the values, we have:
Time = 2,400 miles / 450 mph
Simplifying, we find:
Time = 5.333 hours
Now, we can substitute the known values into the first equation:
Ground Speed = 450 mph + Wind Speed
2,400 miles / 5.333 hours = 450 mph + Wind Speed
Solving for Wind Speed:
Wind Speed = (2,400 miles / 5.333 hours) - 450 mph
Calculating this expression, we find:
Wind Speed ≈ 104.5 mph
Therefore, the speed of the wind is approximately 104.5 mph.