Respuesta :
Answer:
(x,y,t) = (70,70,4)
Step-by-step explanation:
For the first balloon,
Initial height = 10 m.
Rate at which it is going up = 15 m/min.
So, its height x at any time can be given by,
x = 10 + 15t -(1) , where t is in minutes.
For the second balloon,
Initial height = 150 m.
Rate at which it is going downwards = 20 m/min.
so, its height y at any time is given by,
y = 150 - 20t -(2), where t is any minutes
Thus, when both of them will be at same height , x= y.
So, 10 + 15t = 150 - 20t
35t = 140.
t = 4 min.
x = y = 10 + 60 = 70 m.
So, Solution is (x,y,t) = (70 , 70 , 4)
Answer:
(4, 70)
Step-by-step explanation:
Let's call
x: time, in minutes
y: height of the balloon, in meters
The height of the rising balloon is modeled as follows:
y = 15x + 10 (eq. 1)
The height of the descending balloon is modeled as follows:
y = -20x + 150 (eq. 2)
Combining equations 1 and 2:
15x + 10 = -20x + 150
15x + 20x = 150 - 10
35x = 140
x = 140/35 = 4
Replacing it in equation 1:
y = 15(4) + 10 = 70
So, the solution is (4, 70), that is, after 4 minutes both balloons will have the same height, which is 70 meters.
