Flying to Kampala with a tailwind a plane

Nailah Jones

Nailah Jones

Answered question

2022-08-27

Flying to Kampala with a tailwind a plane averaged 158 km/h. On the return trip the plane only averaged 112 km/h while flying back into the same wind. Find the speed of the wind and the speed of the plane in still air.

Answer & Explanation

karton

karton

Expert2023-05-25Added 613 answers

To solve the given problem, let's assume that 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.
When the plane is flying with a tailwind, its effective speed is increased by the speed of the wind. Therefore, the speed of the plane with the tailwind is (p+w) km/h.
On the return trip, when the plane is flying against the wind, its effective speed is decreased by the speed of the wind. Therefore, the speed of the plane against the wind is (pw) km/h.
According to the problem, the plane averaged 158 km/h while flying to Kampala with a tailwind. We can write this as:
(p+w)=158
Similarly, the plane averaged 112 km/h while flying back into the same wind. We can write this as:
(pw)=112
Now we have a system of two equations with two unknowns. We can solve these equations to find the values of p and w.
Let's start by adding the two equations together to eliminate the variable w:
(p+w)+(pw)=158+112
Simplifying the left side and right side of the equation:
2p=270
Dividing both sides of the equation by 2:
p=135
Now that we have found the value of p, we can substitute it back into one of the original equations to find the value of w. Let's use the equation (p+w)=158:
(135+w)=158
Subtracting 135 from both sides of the equation:
w=158135
Simplifying the right side:
w=23
Therefore, the speed of the plane in still air is 135 km/h, and the speed of the wind is 23 km/h.

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