Robin flies to San Francisco from LA in 4 hours. she flies back in 3 hours. if the wind is blowing from the north at velocity of 20mph during both flights, what was the airspeed of the plane (it's speed in the air)?
Well, I must say, Robin sure knows how to fly with the wind! Let's get down to some mathematical circus tricks, shall we?
Since the wind is blowing in the opposite direction for both flights, we need to take that into account. Let's assume the plane's airspeed, which we're trying to find, is represented by "x" mph.
During the flight from LA to San Francisco, the plane is flying against the wind. So, the effective speed of the plane can be calculated as (x - 20) mph.
On the way back from San Francisco to LA, the plane is now flying with the wind. Therefore, the effective speed of the plane becomes (x + 20) mph.
Now, we can set up a simple equation based on the given time and distance:
Distance = Speed × Time
Let's call the distance between LA and San Francisco "D". So, we have:
D = (x - 20) mph × 4 hours
D = (x + 20) mph × 3 hours
Since the distance remains the same for both flights (going and returning), we can equate the two equations:
(x - 20) mph × 4 hours = (x + 20) mph × 3 hours
Now, time for some algebraic acrobatics! Let's solve this equation:
4x - 80 = 3x + 60
4x - 3x = 80 + 60
x = 140 mph
So, after all the calculations, the airspeed of the plane (its speed in the air) is a whopping 140 mph! I hope this flight didn't cause too much turbulence in your brain!
To find the airspeed of the plane, we need to consider the effects of wind on the flight.
Let's assume that the distance between LA and San Francisco is D miles.
During the flight from LA to San Francisco:
The total time taken is 4 hours.
The wind is blowing from the north at a velocity of 20 mph.
We know that the plane's airspeed is the speed at which the plane moves in the air.
Let's assume the airspeed of the plane is x mph.
During this flight, the plane is flying against the wind. Therefore, its effective ground speed will be the difference between its airspeed and the wind speed.
So, the ground speed of the plane during the flight from LA to San Francisco is (x - 20) mph.
Using the formula: Distance = Speed * Time,
we can write the equation: D = (x - 20) * 4.
Similarly, during the flight back from San Francisco to LA:
The total time taken is 3 hours.
The plane is flying with the wind, which means its effective ground speed will be the sum of its airspeed and the wind speed.
So, the ground speed of the plane during the flight back is (x + 20) mph.
Using the same formula: Distance = Speed * Time,
we can write the equation: D = (x + 20) * 3.
Now, we have two equations:
1) D = (x - 20) * 4
2) D = (x + 20) * 3
We can solve these equations simultaneously to find the airspeed of the plane (x).
To find the airspeed of the plane, we need to first understand the concept of groundspeed. Groundspeed is the speed of an aircraft with respect to the ground. It is the combination of the aircraft's airspeed and the speed of the wind.
In this case, we know that the wind is blowing from the north at a velocity of 20 mph during both flights. Let's assume that Robin's airspeed (speed in the air) is represented by "A" mph.
When Robin is flying from LA to San Francisco, she is flying against the wind. This means that the wind is opposing her motion. During this flight, her effective speed (groundspeed) will be the airspeed minus the wind speed.
Groundspeed (from LA to San Francisco) = Airspeed (A) - Wind speed (20 mph)
Similarly, when Robin is flying back from San Francisco to LA, she is flying with the wind. This means that the wind is assisting her motion. During this flight, her effective speed (groundspeed) will be the airspeed plus the wind speed.
Groundspeed (from San Francisco to LA) = Airspeed (A) + Wind speed (20 mph)
We are given that the flight from LA to San Francisco took 4 hours and the flight from San Francisco to LA took 3 hours.
So, we have two equations:
Groundspeed (from LA to San Francisco) = Airspeed (A) - Wind speed (20 mph) ... (1)
Groundspeed (from San Francisco to LA) = Airspeed (A) + Wind speed (20 mph) ... (2)
From equation (1), we can write:
Airspeed (A) = Groundspeed (from LA to San Francisco) + Wind speed (20 mph)
And from equation (2), we can write:
Airspeed (A) = Groundspeed (from San Francisco to LA) - Wind speed (20 mph)
Since both these equations represent the airspeed (A), we can equate them:
Groundspeed (from LA to San Francisco) + Wind speed (20 mph) = Groundspeed (from San Francisco to LA) - Wind speed (20 mph)
By rearranging the equation, we can isolate the groundspeeds:
Groundspeed (from LA to San Francisco) = Groundspeed (from San Francisco to LA) - 2 * Wind speed (20 mph)
Now, we have two equations with only groundspeeds that we can calculate:
Groundspeed (from LA to San Francisco) = Distance (between LA and San Francisco) / Time (taken from LA to San Francisco)
Groundspeed (from San Francisco to LA) = Distance (between San Francisco and LA) / Time (taken from San Francisco to LA)
By substituting these values into the equation, we can solve for the groundspeed from LA to San Francisco.
Finally, to find the airspeed of the plane (A), we substitute the obtained groundspeed from LA to San Francisco (which excludes wind speed) into either equation (1) or (2) and solve for A.
since distance = speed * time
4(s-20) = 3(s+20)
and we know what airspeed: it's its speed in the air. (note apostrophe)
I think we are to assume that San Francisco is just about north of LA
airspeed of plane ---- x mph
speed from SF to LA --- x + 20
speed from LA to SF ---- x - 20
distance one way = 4(x-20)
distance the other way = 3(x+20)
same distance, so
4x - 80 = 3x + 60
x = 140
speed of plane was only 140 mph ???
check:
4(120) =480
3(160) = 480