Final answer:
To determine when both kites will be at the same height, we set up equations based on their starting heights and rising rates and solve for time, t. The calculations show that the kites will be at the same height after 8 seconds.
Step-by-step explanation:
To determine how many seconds it will take for the two kites to be at the same height, we can set up an equation for each kite using the information we have about their initial heights and rates of ascent.
The small kite starts at 7.3 meters and rises at a rate of 2.9 meters per second, so the height of the small kite after t seconds can be represented as:
Hkite1 = 7.3 + 2.9t
The large kite starts at 18.5 meters and rises at a rate of 1.5 meters per second, so the height of the large kite after t seconds can be represented as:
Hkite2 = 18.5 + 1.5t
For the kites to be at the same height, Hkite1 = Hkite2. We equate the two expressions to get:
7.3 + 2.9t = 18.5 + 1.5t
(Subtract 1.5t from both sides)
7.3 + 1.4t = 18.5
(Subtract 7.3 from both sides)
1.4t = 11.2
(Divide both sides by 1.4)
t = 8
Therefore, it will take the kites 8 seconds to reach the same height.