A plane flys 425 miles with the wind and 350 miles against the wind in the same length of time if the speed of the wind is 15 mph what is the speed of the plane
To determine the speed of the plane, we can set up a system of equations using the given information.
Let's denote the speed of the plane as "p" (in mph).
When the plane is flying with the wind, its effective speed would be the sum of the plane's speed and the speed of the wind. So, the effective speed with the wind would be (p + 15) mph.
When the plane is flying against the wind, its effective speed would be the difference between the plane's speed and the speed of the wind. So, the effective speed against the wind would be (p - 15) mph.
We know that the distance traveled with the wind is 425 miles, and the distance traveled against the wind is 350 miles. Since speed is equal to distance divided by time, we can use the formula:
Speed = Distance / Time
Now, since the time taken is the same for both scenarios, we can set up the following equations:
425 = (p + 15) * Time ...(Equation 1)
350 = (p - 15) * Time ...(Equation 2)
To solve for "p," we need to eliminate the variable "Time" from the equations. We can do this by dividing Equation 1 by Equation 2:
425 / 350 = (p + 15) / (p - 15)
Now, we can cross-multiply to solve for "p":
425(p - 15) = 350(p + 15)
Simplifying this equation:
425p - 6375 = 350p + 5250
Combining like terms:
425p - 350p = 5250 + 6375
75p = 11625
Dividing both sides by 75:
p = 155
Therefore, the speed of the plane is 155 mph.
since time = distance/speed,
425/(s+15) = 350/(s-15)
s = 155