A plane will normally cover 52 km in 12 min in still air. On one trip she flew with the wind for 2.5 hr. returning, she still had 100 km to go after 3.5 hr. what was the wind speed?
To determine the wind speed, we can use the formula for the distance covered by the plane with or against the wind.
Let's denote the speed of the plane in still air as 'p' and the wind speed as 'w'.
We are given that the plane normally covers 52 km in 12 minutes in still air. Converting 12 minutes to hours, we get 12/60 = 0.2 hours.
With the wind, the plane flew for 2.5 hours and covered a certain distance. We can express this distance as (p + w) * 2.5 km.
On the return trip, against the wind, the plane covered 100 km in 3.5 hours. This can be expressed as (p - w) * 3.5 km.
Using this information, we can set up two equations:
(p + w) * 2.5 = total distance flown with the wind
(p - w) * 3.5 = 100 km
Now, we can solve these equations simultaneously to find the values of 'p' and 'w'.
Expanding the equations gives us:
2.5p + 2.5w = total distance flown with the wind
3.5p - 3.5w = 100
To eliminate the 'w' terms, we can multiply the second equation by 2.5 and add it to the first equation:
2.5p + 2.5w + 8.75p - 8.75w = total distance flown with the wind + 250
Combining like terms:
11.25p - 6.25w = total distance flown with the wind + 250
Since we don't have the exact value for the total distance flown with the wind, we can't directly solve for 'p' and 'w'. However, we can simplify the equation further.
Now, substitute the known values for the total distance flown with the wind and solve for 'w':
11.25p - 6.25w = total distance flown with the wind + 250
11.25p - 6.25w = (p + w) * 2.5 + 250
We can substitute 'p = 52 km/0.2 hr' into the equation:
11.25 * (52/0.2) - 6.25w = (52/0.2 + w) * 2.5 + 250
Simplifying further should give us the wind speed 'w'.