Two planes took off from a Chicago airport flying in opposite directions. One plane traveled 30mph faster than the other. They were 1500 miles apart after 2hrs. How fast was each flying
If one's speed = x, then the other's speed = x+30.
2x + 2(x+30) = 1500
Solve for x and x+30.
One is traveling 360 mph and the other is traveling 390 mph.
Let's assume the speed of the slower plane is "x" mph.
According to the given information, the speed of the faster plane is x + 30 mph.
In 2 hours, the slower plane will have traveled a distance of 2x miles (speed multiplied by time).
In 2 hours, the faster plane will have traveled a distance of 2(x + 30) miles.
Since they are flying in opposite directions, the sum of their distances traveled will be equal to the total distance of 1500 miles.
Therefore, we can write the equation: 2x + 2(x + 30) = 1500.
Simplifying the equation, we get: 2x + 2x + 60 = 1500.
Combining like terms: 4x + 60 = 1500.
Subtracting 60 from both sides: 4x = 1440.
Dividing both sides by 4: x = 360.
So, the speed of the slower plane is 360 mph.
The speed of the faster plane is x + 30 = 360 + 30 = 390 mph.
To find the speed of each plane, let's first assign variables to the unknowns. Let P1 represent the speed of the slower plane in miles per hour (mph), and P2 represent the speed of the faster plane.
Since the slower plane is traveling at P1 mph, and the faster plane is traveling 30mph faster, it is traveling at P1 + 30 mph.
We are given that after 2 hours, the two planes are 1500 miles apart. This means that, when added together, the distances traveled by both planes in 2 hours should equal 1500 miles.
The distance traveled by the slower plane can be calculated by multiplying its speed (P1 mph) by the time (2 hours). Similarly, the distance traveled by the faster plane can be calculated by multiplying its speed (P1 + 30 mph) by the time (2 hours).
Therefore, we can set up the equation:
Distance traveled by the slower plane + Distance traveled by the faster plane = 1500 miles
(P1 * 2) + ((P1 + 30) * 2) = 1500
Simplify the equation:
2P1 + 2P1 + 60 = 1500
Combine like terms:
4P1 + 60 = 1500
Subtract 60 from both sides:
4P1 = 1440
Divide both sides by 4 to isolate P1:
P1 = 1440 / 4 = 360 mph
So, the slower plane is flying at a speed of 360 mph.
To find the speed of the faster plane, we can substitute the value of P1 back into the equation:
P2 = P1 + 30
P2 = 360 + 30 = 390 mph
Therefore, the faster plane is flying at a speed of 390 mph.