two planes which are 1695 miles apart fly towards each other,their speeds differ by 65 mph,if they pass each other in 3 hours, what is the speed of each
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Let's say the speed of the first plane is x mph.
According to the given information, the speed of the second plane will be (x + 65) mph, as the speeds differ by 65 mph.
Now, let's calculate the total distance traveled by both planes in 3 hours:
Distance = Speed × Time
For the first plane: Distance = x mph × 3 hours = 3x miles
For the second plane: Distance = (x + 65) mph × 3 hours = 3(x + 65) miles
Since they are flying towards each other, the sum of their distances should equal the total distance between them:
3x + 3(x + 65) = 1695
Now, let's solve the equation:
3x + 3x + 195 = 1695
Combining like terms:
6x + 195 = 1695
Subtracting 195 from both sides:
6x = 1500
Dividing both sides by 6:
x = 250
Therefore, the speed of the first plane is 250 mph, and the speed of the second plane is (250 + 65) mph = 315 mph.
To find the speeds of the two planes, let's use the following steps:
Step 1: Assign variables
Let's assign variables to the speeds of the planes. Let's call the speed of the first plane "x" mph and the speed of the second plane "y" mph.
Step 2: Create an equation based on distances traveled
We know that the planes are 1695 miles apart and they pass each other after 3 hours. In this time, the first plane will have traveled a distance of 3x miles, and the second plane will have traveled a distance of 3y miles. Since the total distance they travel is 1695 miles, we can create the equation:
3x + 3y = 1695
Step 3: Incorporate the speed difference
We also know that the speeds of the planes differ by 65 mph. Thus, we can write another equation:
x - y = 65
Step 4: Solve the equations
We now have a system of equations:
3x + 3y = 1695
x - y = 65
We can solve this system of equations using substitution or elimination.
Let's use the elimination method to solve it. Multiply the second equation by 3 to cancel out the "y" term:
3(x - y) = 3(65)
3x - 3y = 195
Now, add this equation to the first equation:
(3x + 3y) + (3x - 3y) = 1695 + 195
6x = 1890
Divide both sides of the equation by 6:
x = 315
Step 5: Calculate the other speed
Now that we have the value for "x," which represents the speed of the first plane, we can substitute this value into one of the original equations to solve for "y."
Let's use the first equation:
3x + 3y = 1695
3(315) + 3y = 1695
945 + 3y = 1695
3y = 750
y = 250
Therefore, the speed of the first plane is 315 mph, and the speed of the second plane is 250 mph.