Plane A leaves the airport. One hour later, Plane B leaves the same airport on the same course. It catches up to Plane A in 2.5 hours. The average speed of Plane B is 300km/h faster than Plane A. Find the speed of each plane.
Recall that speed is distance traveled over time:
v = d/t
Represent the speeds with variables:
Let x = speed of Plane A
Since it was said the speed of Plane B is 300 km/h faster than Plane A,
Let x + 300 = speed of Plane B
When they catch up, that means that their distance traveled is the same, so we will equate their distance traveled.
v = d/t
d = v*t
Plane A:
d = x * (2.5 + 1)
Note that the total time traveled by Plane A is 2.5 + 1 because it is one hour ahead of Plane B, and Plane B caught up with it after 2.5 hours.
Plane B:
d = (x + 300) * 2.5
Equating,
x * (2.5 + 1) = (x + 300) * 2.5
3.5x = 2.5x + 750
3.5 x - 2.5x = 750
x = 750 km/h (Plane A speed)
x+300 = 1050 km/h (Plane B speed)
hope this helps~ `u`
Thanks so much! This helped a lot
Let's assume the speed of Plane A is x km/h.
Since Plane B catches up to Plane A in 2.5 hours, we can set up the equation:
2.5 * (x + 300) = 2.5x
Now, let's solve for x:
2.5x + 750 = 2.5x
Subtract 2.5x from both sides:
750 = 2.5x - 2.5x
750 = 0
This is not a valid equation, which means there is no solution.
Therefore, there is an error in the problem statement or the values provided. Please double-check the given information.
To find the speed of each plane, let's assign variables. Let's assume the speed of Plane A is "x" km/h. Since Plane B is 300 km/h faster, its speed will be "x + 300" km/h.
Now, let's use the formula:
Distance = Speed × Time
We know that Plane B catches up to Plane A in 2.5 hours. Therefore, the distance traveled by Plane A is the same as the distance traveled by Plane B in this time.
Distance traveled by Plane A = Distance traveled by Plane B
To find the distance, we can use the formula again:
Distance = Speed × Time
For Plane A, the distance is (x km/h) × (2.5 hours) = 2.5x km.
For Plane B, the distance is (x + 300 km/h) × (2.5 hours) = 2.5(x + 300) km.
Since the distances are equal, we can set up an equation as follows:
2.5x = 2.5(x + 300)
Now, let's solve for x:
2.5x = 2.5x + 750
Subtracting 2.5x from both sides:
0 = 750
Wait a minute, we have reached a contradiction (0=750), which means there is no solution to this problem. It seems there might be some incorrect information or missing details in the question. Please double-check the given information and try again.