Flying to Kampala with a tailwind a plane average 158km/h. On the return trip the plane only averaged 112km/h while flying back into the same wind. Find the speed of the wind and the speed of the plane in still air.
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speed of plane in still air --- x mph
speed of wind ------------ y mph
so going with the wind, speed = x+y
against the wind, speed = x-y
x+y = 158
x-y = 112
add them
2x = 270
x = 135
then 135 + y = 158
y = 23
speed of wind is 23 mph, speed of plane in still air = 135 mph
Let's assume the speed of the plane in still air is represented by "p" km/h, and the speed of the wind is represented by "w" km/h.
On the flight to Kampala, with the tailwind, the effective speed of the plane will be increased by the speed of the wind. Therefore, the speed of the plane can be expressed as "p + w" km/h.
On the return trip, flying against the wind, the effective speed of the plane will be reduced by the speed of the wind. Therefore, the speed of the plane can be expressed as "p - w" km/h.
Given that the plane averages 158 km/h with a tailwind, we can set up the following equation:
(p + w) = 158 ---- (1)
Similarly, given that the plane averages 112 km/h while flying back into the same wind, we can set up another equation:
(p - w) = 112 ---- (2)
Now, we can solve this system of equations to find the values of "p" and "w".
From equation (1), we can rearrange it to solve for "p":
p = 158 - w
Substituting this value of "p" into equation (2), we get:
(158 - w) - w = 112
Simplifying:
158 - w - w = 112
158 - 2w = 112
-2w = 112 - 158
-2w = -46
Dividing both sides by -2:
w = -46 / -2
w = 23
Therefore, the speed of the wind is 23 km/h.
Now, substitute this value of "w" into equation (1) to find the speed of the plane in still air:
p + 23 = 158
Simplifying:
p = 158 - 23
p = 135
Therefore, the speed of the plane in still air is 135 km/h.
In summary, the speed of the wind is 23 km/h, and the speed of the plane in still air is 135 km/h.
To find the speed of the wind and the speed of the plane in still air, we can set up a system of equations based on the given information.
Let's denote the speed of the plane in still air as "p" and the speed of the wind as "w".
When the plane is flying with the tailwind (wind in the same direction as the plane's motion), the effective speed of the plane will be the sum of its speed in still air and the speed of the wind. So, we have the equation:
p + w = 158 km/h -- (Equation 1)
On the return trip, the plane is flying against the wind (headwind). In this case, the effective speed of the plane will be the difference between its speed in still air and the speed of the wind. So, we have:
p - w = 112 km/h -- (Equation 2)
Now we have a system of equations (Equation 1 and Equation 2) that we can solve simultaneously to find the values of "p" and "w".
To eliminate "w", we can add Equation 1 and Equation 2:
(p + w) + (p - w) = 158 + 112
By simplifying the equation, we get:
2p = 270
Now, we can solve for "p" by dividing both sides of the equation by 2:
p = 135 km/h
Now that we have the value of "p", we can substitute it back into Equation 1 or Equation 2 to find the value of "w". Let's use Equation 1:
135 + w = 158
By rearranging the equation, we get:
w = 158 - 135
w = 23 km/h
Therefore, the speed of the wind is 23 km/h and the speed of the plane in still air is 135 km/h.