Final answer:
To determine when the red kite will be higher than the blue kite, their respective heights as functions of time are equated and solved for t, which yields approximately 9.67 seconds. Rounded to the nearest second, it takes 10 seconds for the red kite to be higher.
Step-by-step explanation:
To find out how long it will take for the red kite to be higher than the blue kite, we need to calculate the height of each kite as a function of time and then determine when the height of the red kite will surpass that of the blue kite.
The red kite starts at 103 feet and rises at 7 feet per second. So, its height as a function of time is:
Heightred(t) = 103 + 7t
The blue kite starts at 132 feet and rises at 4 feet per second. So, its height as a function of time is:
Heightblue(t) = 132 + 4t
To find the time when the red kite is higher than the blue kite, we can set their heights equal and solve for t:
103 + 7t = 132 + 4t
7t - 4t = 132 - 103
3t = 29
t = 29/3
t ≈ 9.67 seconds
Rounded to the nearest second, the red kite will be higher than the blue kite in 10 seconds.