With an 80 km/h head wind a plane can fly a certain distance in 4 h. Flying in the opposite direction, with the same wind blowing, it can fly that distance in one hour less. What is the plane’s speed?
since distance = speed * time,
(s-80)(4) = (s+80)(3)
To find the plane's speed, we can use the concept of relative velocity. Let's assume the speed of the plane in still air is 'p' km/h.
When the plane flies with an 80 km/h headwind, its effective speed decreases by 80 km/h. So, the plane's speed in that situation will be (p - 80) km/h. We are given that the plane flies a certain distance in 4 hours with this headwind.
Using the formula distance = speed × time, we can write the equation for the first scenario as:
Distance = (p - 80) km/h × 4 h
Now, when the plane flies in the opposite direction with the same 80 km/h wind, its effective speed increases by 80 km/h. So, the plane's speed in this situation will be (p + 80) km/h. We are given that the plane flies the same distance, but 1 hour less than in the first scenario.
Using the formula distance = speed × time, we can write the equation for the second scenario as:
Distance = (p + 80) km/h × (4 - 1) h
Since the distances are the same in both scenarios, we can set the two equations equal to each other:
(p - 80) km/h × 4 h = (p + 80) km/h × 3 h
Now we can solve this equation to find the value of 'p', which represents the plane's speed in still air.
Expanding the equation:
4p - 320 = 3p + 240
Simplifying:
4p - 3p = 240 + 320
p = 560
Therefore, the plane's speed in still air is 560 km/h.