Question

Two small planes start from the same point and fly in opposite directions. The first plane is flying 25 mph slower than the second plane. In two hours, the planes are 430 miles apart. Find the rate of each plane.

Answer 1

The rate of the faster plane is 120 mph, and the rate of the slower plane is 95 mph, derived by setting up an equation that accounts for both planes flying in opposite directions and being 430 miles apart after 2 hours.

Step-by-step explanation:

To solve the problem involving two planes flying in opposite directions, we use the concept that their rates add up when they are moving away from each other. Let's define the rate of the faster plane as x mph.

Then the rate of the slower plane would be x - 25 mph.

Since they are flying in opposite directions for 2 hours and are 430 miles apart, we can express this relationship as:

2x (for the faster plane) + 2(x - 25) (for the slower plane) = 430

This gives us the equation:

2x + 2x - 50 = 430

Combining like terms and solving for x:

4x - 50 = 430

4x = 480

x = 120

Thus, the rate of the faster plane is 120 mph and the rate of the slower plane is 95 mph (120 mph - 25 mph).