Ask Question
22 August, 13:48

A hot air balloon is 10 meters above the ground and rising at a rate of 15 meters per minute. Another balloon is 150 meters above the ground and descending at a rate of 20 meters per minute. What is the solution of the system of equations? Make sure you write the answer as an ordered pair.

+1
Answers (2)
  1. 22 August, 13:50
    0
    (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)
  2. 22 August, 14:10
    0
    (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.
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “A hot air balloon is 10 meters above the ground and rising at a rate of 15 meters per minute. Another balloon is 150 meters above the ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers