Flying with the wind, a plane traveled 570 miles in 3 hours. Flying against the wind, the plane traveled the same distance in 5 hours. Find the rate of the plane in calm air and the rate of the wind.
Rate of plane ______mph
Rate of wind ________mph
See previous post: Sat, 12-6-14, 2:02 PM
To find the rate of the plane in calm air and the rate of the wind, we can set up a system of equations based on the given information.
Let's assume the rate of the plane in calm air is x mph and the rate of the wind is y mph.
When the plane is flying with the wind, the effective speed of the plane is the sum of the plane's speed in calm air and the wind's speed. So, the equation for this scenario is:
x + y = 570/3
x + y = 190
When the plane is flying against the wind, the effective speed of the plane is the difference between the plane's speed in calm air and the wind's speed. So, the equation for this scenario is:
x - y = 570/5
x - y = 114
Now we have a system of equations:
x + y = 190
x - y = 114
To solve this system, we can use the method of elimination. Adding the two equations together will eliminate the variable "y":
(x + y) + (x - y) = 190 + 114
2x = 304
x = 152
Now we can substitute the value of x back into one of the equations to solve for y:
152 + y = 190
y = 190 - 152
y = 38
Therefore, the rate of the plane in calm air is 152 mph and the rate of the wind is 38 mph.