a small plane flying into the wind takes 3 hrs 20 min to complete a flight of 960 km. Flying with the wind the same plane takes 2 h 30 min to make the trip.what is the speed of the plane? what is the speed of the wind?
can u plz finish the whole question??
with the speed,time, distance graph?
plane -- x
wind -- y
960/(x-y) = 10/3 (#1)
960/(x+y) = 2.5 (#2)
#1
2.5(x+y) = 960
5x+ 5y = 1920
#2
10/3(x-y) = 960
10x+10y = 2880
2(#1)
10x + 10y = 3840
#2 : 10x-10y = 2880
add them
20x = 6720
x=336
sub back in simplest #1
5(336) + 5y = 1920
y = 48
check:
with wind: 960/(336+48) = 2.5
against: 960/(336-48) = 10/3 ... YEAH
To find the speed of the plane and the speed of the wind, we can set up a system of equations.
Let's assume the speed of the plane is represented by "p" and the speed of the wind is represented by "w".
When the plane is flying against the wind, the effective speed will be reduced. So, the time taken to complete the flight will be greater. According to the given information, it takes 3 hours and 20 minutes (or 3.33 hours) to complete a flight of 960 km. We can write this as:
960 = (p - w) * 3.33
When the plane is flying with the wind, the effective speed will be increased. So, the time taken to complete the flight will be less. It takes 2 hours and 30 minutes (or 2.5 hours) to make the trip of 960 km. We can write this as:
960 = (p + w) * 2.5
Now, we have a system of equations:
1) 960 = (p - w) * 3.33
2) 960 = (p + w) * 2.5
Let's solve these equations to find the values of "p" and "w".
We can simplify equation 1 by dividing both sides by 3.33:
288.29 = p - w
Next, we can simplify equation 2 by dividing both sides by 2.5:
384 = p + w
Now we have two equations:
3) 288.29 = p - w
4) 384 = p + w
We can solve this system by adding equations 3 and 4:
288.29 + 384 = (p - w) + (p + w)
672.29 = 2p
Dividing both sides by 2:
p = 336.15
Now we can substitute the value of "p" back into one of the equations, let's use equation 4 to find the value of "w":
384 = 336.15 + w
Rearranging the equation:
w = 384 - 336.15
w = 47.85
So, the speed of the plane is approximately 336.15 km/h, and the speed of the wind is approximately 47.85 km/h.
Now let's create a speed-time-distance graph to visualize the information:
On the x-axis, we will plot time in hours, and on the y-axis, we will plot speed in km/h.
For the flight against the wind:
Time = 3 hours and 20 minutes = 3.33 hours
Speed = plane speed - wind speed = p - w = 336.15 - 47.85 = 288.3 km/h
Distance = 960 km
Plotting these values on the graph, we get a line that starts at the origin (0, 0) and intersects the point (3.33, 288.3).
For the flight with the wind:
Time = 2 hours and 30 minutes = 2.5 hours
Speed = plane speed + wind speed = p + w = 336.15 + 47.85 = 384 km/h
Distance = 960 km
Plotting these values on the graph, we get a line that starts at the origin (0, 0) and intersects the point (2.5, 384).
Now you have the speed of the plane, the speed of the wind, and a visual representation of the speed-time-distance graph.