Flying against the wind, a jet travels 2340 miles in 3 hours. Flying with the wind, the same jet travels 8960 miles in 7 hours. What is the rate of the jet in still air and what is the rate of the wind?
Vp - Vw = 2340/3 = 780 mi/h.
Vp + Vw = 8960/7 = 1280 mi/h.
Vp + Vw = 1280.
Vp - Vw = 780
Solve for Vw and Vp.
To find the rate of the jet in still air and the rate of the wind, we can set up a system of equations.
Let's assume the rate of the jet in still air is represented by 'J' and the rate of the wind is represented by 'W'.
When flying against the wind, the effective speed of the jet is reduced, so the equation becomes:
(J - W) * 3 = 2340
When flying with the wind, the effective speed of the jet is increased, so the equation becomes:
(J + W) * 7 = 8960
Now, we can solve this system of equations simultaneously to find the values of J and W.
From the first equation, we have:
3J - 3W = 2340
From the second equation, we have:
7J + 7W = 8960
To eliminate W, we can multiply the first equation by 7 and the second equation by 3:
21J - 21W = 16380
21J + 21W = 26880
Now, let's add the two equations:
(21J - 21W) + (21J + 21W) = 16380 + 26880
42J = 43260
Next, we can solve for J by dividing both sides of the equation by 42:
J = 43260 / 42
J = 1030
Now, substitute the value of J back into one of the original equations, such as the first one:
(1030 - W) * 3 = 2340
3090 - 3W = 2340
Solve for W by isolating W:
-3W = 2340 - 3090
-3W = -750
W = -750 / -3
W = 250
Therefore, the rate of the jet in still air (J) is 1030 mph and the rate of the wind (W) is 250 mph.
To find the rate of the jet in still air and the rate of the wind, we can use a system of equations.
Let's assume the rate of the jet in still air is represented by "J" and the rate of the wind is represented by "W".
Against the wind, the jet travels 2340 miles in 3 hours. This means that the effective speed of the jet is the rate of the jet in still air minus the rate of the wind. So, the equation for this scenario is:
2340 miles = (J - W) * 3 hours ----> Equation 1
With the wind, the jet travels 8960 miles in 7 hours. This means that the effective speed of the jet is the rate of the jet in still air plus the rate of the wind. So, the equation for this scenario is:
8960 miles = (J + W) * 7 hours ----> Equation 2
We now have a system of equations that can be solved to find the values of J and W.
To solve this system of equations, we can use the method of substitution. Rearrange Equation 1 to solve for J:
(J - W) = 2340 miles / 3 hours
J - W = 780 mph ----> Equation 3
Now, substitute the value of (J - W) in Equation 3 into Equation 2:
(J + W) * 7 hours = 8960 miles
J + W = 8960 miles / 7 hours
J + W = 1280 mph ----> Equation 4
We now have a system of equations:
J - W = 780 mph ----> Equation 3
J + W = 1280 mph ----> Equation 4
Add Equations 3 and 4 together:
(J + W) + (J - W) = 780 mph + 1280 mph
2J = 2060 mph
Divide both sides by 2:
J = 1030 mph
Now, substitute the value of J back into Equation 4 to find W:
1030 mph + W = 1280 mph
W = 1280 mph - 1030 mph
W = 250 mph
So, the rate of the jet in still air is 1030 mph, and the rate of the wind is 250 mph.
If the plane's speed is p
and the wind's speed is w,
then since distance = speed * time,
3(p-w) = 2340
7(p+w) = 8960
Now just solve for p and w.