Final answer:
The second jet will overtake the first one in approximately 1.57 hours or 1 hour and 34 minutes after the second jet departs from the Charlotte, North Carolina, airport.
Step-by-step explanation:
To determine how long the second jet will take to overtake the first jet, we can set up an equation that represents the position of each jet as a function of time. Let's denote t as the time that has passed since the second jet left. Since the first jet leaves half an hour earlier, it has been flying for t + 0.5 hours. The first jet's distance covered can be calculated by multiplying its speed, 564 km/h, by t + 0.5. Therefore, the distance of the first jet is d1 = 564(t + 0.5).
The second jet's distance covered is its speed, 744 km/h, multiplied by the time, t, since it left. So, its distance is d2 = 744t. To find out when the second jet overtakes the first jet, we set their distances equal: 564(t + 0.5) = 744t. Solving for t gives us the time it will take for the second jet to catch up.
Solve for t:
564t + 282 = 744t
744t - 564t = 282
180t = 282
t = 282/180
t = 1.5667 hours
The second jet will overtake the first jet in approximately 1.57 hours, which is about 1 hour and 34 minutes.