a jet leaves the Charlotte, North Carolina, airport traveling at an average rate of 564 km/h. Another jet leaves the airport one half hour later traveling 722 km/h in the same direction. How long will the second jet take to overtake the first?
let time of 1st jet be t hrs
then time of 2nd jet = t-1/2 hrs
distance of 1st = 564t
distance of 2nd = 722(t-1/2) = 722t - 361
but they went the same distance, so ...
564t = 722t - 361
-158t = -361
t = 2.285 hrs
so the 2nd takes 2.285 - .5 hrs
= 1.785 hrs or 1 hour and 47 minutes
To determine how long it will take for the second jet to overtake the first, we need to calculate the time it takes for the two jets to cover the same distance.
Let's start by finding the head start distance of the first jet. Since it started half an hour earlier than the second jet, it traveled for that amount of time at its average rate. The formula to calculate the distance is:
Distance = Rate × Time
Distance of the head start = 564 km/h × 0.5 h
Distance of the head start = 282 km
Now, we can set up an equation to find out when the second jet will catch up with the first. Let's assume the time taken by the second jet to catch up is represented by t hours.
For the second jet:
Distance = Rate × Time
Distance of the second jet = 722 km/h × t
Since the first jet has a head start, the distance it travels will be the same as the distance the second jet travels when they meet. So, we have:
Distance of the first jet + Distance of the second jet = Distance of the second jet
282 km + 722 km/h × t = 722 km/h × t
Simplifying the equation, we get:
282 km = 722 km/h × t - 722 km/h × t
282 km = 158 km/h × t
Now, we can solve for t by dividing both sides of the equation by 158 km/h:
t = 282 km / 158 km/h
t ≈ 1.785 hours
Therefore, it will take approximately 1.785 hours (or 1 hour and 47 minutes) for the second jet to overtake the first jet.