Two planes left at the same time from two airports which are 4,500 miles apart and flew toward each other. In 5 hours, they passed each other. The rate of the fast plane was twice the rate of the slow plane. Find the rate of each plane.
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where can i find the correct answer
To find the rate of each plane, let's assign variables to the unknowns:
Let x be the rate of the slower plane (in miles per hour).
Since the faster plane is twice as fast as the slower plane, the rate of the faster plane is 2x (in miles per hour).
Using the formula "distance = rate × time," we can calculate the distance each plane traveled in 5 hours:
Distance traveled by slower plane = rate × time = x × 5 = 5x miles
Distance traveled by faster plane = rate × time = 2x × 5 = 10x miles
Since both planes flew toward each other, the sum of their distances traveled should be equal to the total distance between the airports:
Distance traveled by slower plane + Distance traveled by faster plane = Total distance
5x + 10x = 4500
Now we can solve the equation:
15x = 4500
Dividing both sides of the equation by 15:
x = 4500 / 15
x = 300
So, the rate of the slower plane is x = 300 miles per hour, and the rate of the faster plane is 2x = 2 * 300 = 600 miles per hour.