A plane can fly a certain distance in 6 hours with the wind, but can return only three-fourths the distance in the same time. If the speed of the plane in still air is 200 km per hour, find the velocity of the wind.
let the speed of the wind be x km/h
so distance with the wind = 6(200+x) km
distance against the wind = 6(200-x)
but 6(200-x) = (3/4)(6(200+x))
solve for x , let me know what you get.
to the solution, x (the speed of the wind) is 200/7. But to the answer key it is 80 km/h. I am really confused :/
28.57 km/h
The speed of the wind is indeed 200/7 or 28.57 mph
check:
with the help of the wind the plane is moving at
228.57 mph, for 6 hrs = 1371.43 kkm
against the wind, the plane is moving at 200-28.57 or 171.43 km/h, and for 6 hours that would be 1028.57
and (3/4)(1371.43) = 1028.57
Your answer key of 80 km/h is incorrect
Thanks a lot. I will tell my teacher about this. I spent hours trying to solve this. I feel tricked :)
To solve this problem, we need to set up an equation based on the given information.
Let's define the speed of the wind as 'w' km per hour.
When the plane flies with the wind, its effective speed is increased by the speed of the wind. Therefore, the speed of the plane with the wind is (200 + w) km per hour.
When the plane flies against the wind, its effective speed is decreased by the speed of the wind. Therefore, the speed of the plane against the wind is (200 - w) km per hour.
Now, we can use the formula:
distance = speed × time
For the plane flying with the wind, the distance can be represented as (200 + w) × 6.
For the plane flying against the wind, the distance is (200 - w) × 6, but it is only three-fourths of the distance flown with the wind. Therefore, we can write the equation as:
(200 - w) × 6 = (3/4) * (200 + w) × 6
Simplifying this equation will help us find the value of 'w', the velocity of the wind.
Let's start by simplifying the equation:
6(200 - w) = (3/4) * 6(200 + w)
Expanding both sides of the equation:
1200 - 6w = (3/4) * 1200 + (3/4) * 6w
Now, multiplying both sides of the equation by 4 to eliminate the fraction:
4(1200 - 6w) = 3(1200 + 6w)
Expanding again:
4800 - 24w = 3600 + 18w
Now, let's bring all the terms involving 'w' to one side of the equation:
4800 - 3600 = 18w + 24w
1200 = 42w
Finally, solve for 'w' by dividing both sides of the equation by 42:
w = 1200/42
w ≈ 28.571
Therefore, the velocity of the wind is approximately 28.571 km per hour.