Two small planes start from the same point and fly in the opposite directions. The first plane is flying 35 mph slower than the second plane. In 2 hrs, the planes are 530 mi apart. Find the rate of the slow plane.

To find the rate of the slow plane, we can first set up a system of equations based on the given information.

Let's assume that the rate of the second plane (the faster one) is represented by the variable "x". Therefore, the rate of the first plane (the slower one) would be "x - 35" mph.

We are also given that in 2 hours, the planes are 530 miles apart. Since they are flying in opposite directions, we can add their distances together.

Using the formula speed = distance / time, we can set up the following equation for the faster plane:
speed = distance / time
x = distance / 2

For the slower plane, we can use the same formula:
speed = distance / time
x - 35 = distance / 2

We can now solve this system of equations to find the value of "x", which represents the rate of the fast plane.

To do this, we'll solve the equations simultaneously:

Equation 1: x = distance / 2
Equation 2: x - 35 = distance / 2

Since the distance for both planes is the same (530 miles), we can substitute it into both equations:

Equation 1: x = 530 / 2
Equation 2: x - 35 = 530 / 2

Simplifying further:

Equation 1: x = 265
Equation 2: x - 35 = 265 / 2

Now, we can solve Equation 2:

x - 35 = 265 / 2
Multiply both sides by 2 to get rid of the fraction:
2(x - 35) = 265
2x - 70 = 265
2x = 265 + 70
2x = 335
Divide both sides by 2:
x = 335 / 2
x = 167.5

Therefore, the rate of the fast plane is 167.5 mph.

Since the slow plane is flying 35 mph slower than the fast plane, the rate of the slow plane would be:

167.5 - 35 = 132.5 mph

So, the rate of the slow plane is 132.5 mph.

How would you do it if the planes were goin in the same direction?

147

separation speed = v + v + 35 =2v+35

(2v+35)(2) = 530
You should be able to take it from there.

Thank you

You are welcome :)