A child releases a balloon from a height of 6ft and it ascends at a rate of 5ft per second. A second balloon starts at a height of 51ft and ascends at a rate of 2ft per second. After how many seconds will both balloons be at the same height above the ground?
h=5t+6
h= 2t+51
same height, set them equal, and solve for time t.
Thank you
To find the time when both balloons will be at the same height above the ground, we need to set up equations for the heights of the two balloons as a function of time.
Let's assume t represents the time in seconds.
For the first balloon that starts at a height of 6ft and ascends at a rate of 5ft per second, the height h1 at time t can be represented by the equation:
h1 = 6ft + 5ft/s * t
For the second balloon that starts at a height of 51ft and ascends at a rate of 2ft per second, the height h2 at time t can be represented by the equation:
h2 = 51ft + 2ft/s * t
To find the time when both balloons will be at the same height, we can set the two equations equal to each other and solve for t:
6ft + 5ft/s * t = 51ft + 2ft/s * t
Now, we can solve this equation for t:
5ft/s * t - 2ft/s * t = 51ft - 6ft
3ft/s * t = 45ft
t = 45ft / 3ft/s
t = 15 seconds
Therefore, both balloons will be at the same height above the ground after 15 seconds.