Airplane A travels
1400
km at a certain speed. Plane B travels
1000
km at a speed
50 km divided by h
faster than plane A in 3 hrs less time. Find the speed of each plane.
Plane B travels 1000 km at a speed 50 km
Are you sure u copied the sentence correct cuz the unit of speed is km/hr (m/s) in SI
Airplane A travels
1400 km at a certain speed. Plane B travels
1000
km at a speed
50 km/h faster than plane A in 3 hrs less time. Find the speed of each plane
speed of slower plane --- x km/h
speed of faster plane --- x+50 km/h
1400/x - 1000/(x+50) = 3
times x(x+50)
1400(x+50) - 1000x = 3x(x+50)
1400x + 70000 - 1000x = 3x^2+ 150x
3x^2 - 250x - 70000 = 0
(x - 200)(3x + 350) = 0
x = 200 or a negative, which is rejected
The slower plane can go 200 km/h
the faster one goes 250 km/h
To find the speeds of planes A and B, let's break down the information provided:
Let the speed of plane A be represented by "x" km/h.
The distance traveled by plane A is 1400 km.
So, the time taken by plane A to cover the distance can be calculated using the formula:
Time = Distance / Speed
Therefore, the time taken by plane A is 1400 km / x km/h.
Now let's consider plane B:
Plane B is traveling 50 km/h faster than plane A, so its speed will be (x + 50) km/h.
The distance covered by plane B is 1000 km.
Using the same formula, the time taken by plane B is given by:
Time = Distance / Speed = 1000 km / (x + 50) km/h.
According to the problem, plane B takes 3 hours less than plane A to cover the distance. So we have the equation:
1400 km / x km/h - 1000 km / (x + 50) km/h = 3
To solve this equation, we can cross-multiply and simplify:
[(1400 km)(x + 50) - (1000 km)(x)] / x(x+50) = 3
Expanding and simplifying:
(1400x + 70,000 - 1000x) / (x^2 + 50x) = 3
400x + 70,000 = 3x^2 + 150x
To solve this quadratic equation, we'll rearrange it and set it equal to zero:
3x^2 + 150x - 400x - 70,000 = 0
3x^2 - 250x - 70,000 = 0
Now we can solve for x by factoring, using the quadratic formula, or using a graphing calculator.
Once we find the value of x, we can substitute it into either equation to find the speed of plane B (x + 50 km/h).