An airplane flew for 6 hours with a 22km/hour tailwind. The return flight against the same wind takes 8 hours. Find the speed of the plane with no wind and windspeed.
speed of plane with no wind --- x km/h
speed of wind ----- 22 km/h
distance of first trip = 6(x+22)
distance of return trip = 8(x-22)
but aren't the distances the same ?
take it from here.
To find the speed of the plane with no wind and the speed of the wind, we can set up a system of equations based on the given information.
Let's denote the speed of the plane with no wind as "p" (in km/h) and the speed of the wind as "w" (in km/h).
When the airplane flies with a tailwind, the effective speed of the plane is increased. So the speed of the plane with the tailwind is given by:
p + w = 22 -- Equation 1
On the return flight against the wind, the effective speed of the plane is decreased. So the speed of the plane with the headwind is:
p - w -- Equation 2
We are given that the flight with a tailwind took 6 hours, and the flight against the wind took 8 hours. We can use the time and speed formulas: Distance = Speed × Time
For the flight with the tailwind:
Distance = (p + w) × 6
For the return flight against the wind:
Distance = (p - w) × 8
Since the distances for both flights are the same (going and returning), we have:
(p + w) × 6 = (p - w) × 8
Now we can solve this equation to find the values of p and w.
Expanding the equation gives:
6p + 6w = 8p - 8w
Rearranging the terms gives:
2p = 14w
Dividing both sides by 2 gives:
p = 7w
Substituting the value of p in Equation 1, we get:
7w + w = 22
Combining like terms gives:
8w = 22
Dividing both sides by 8 gives:
w = 2.75 km/h
Since we now know the value of w, we can substitute it back into Equation 1 to find p:
p + 2.75 = 22
Subtracting 2.75 from both sides gives:
p = 19.25 km/h
Therefore, the speed of the plane with no wind is 19.25 km/h, and the speed of the wind is 2.75 km/h.