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 at 744km/h in the same direction. Use an equation to find how long the second jet will take to overtake the first.
Use the fact that at the moment of "overtaking" they would have gone the same distance
Time for slower plane --- t hrs
time for faster plane ---- t-1 hrs
564t = 744(t-1)
continue, solve for t ,
that was a half hour later.
To find out how long it will take for the second jet to overtake the first, we need to set up an equation based on the relative distance between the jets.
Let's assume that the time it takes for the second jet to overtake the first is represented by 't' (in hours). Since the second jet leaves half an hour later than the first one, the first jet will already have been flying for 't + 0.5' hours.
Now, let's calculate the distances traveled by each jet:
Distance traveled by the first jet = Speed of the first jet × Time traveled = 564 km/h × (t + 0.5) h
Distance traveled by the second jet = Speed of the second jet × Time traveled = 744 km/h × t h
Since we are looking for the time when the second jet overtakes the first, the distances traveled by both jets must be equal. Therefore, we can set up the following equation:
564 (t + 0.5) = 744t
Now, let's solve for 't':
564t + 282 = 744t
282 = 744t - 564t
282 = 180t
t = 282 / 180
t ≈ 1.57
Therefore, it will take approximately 1.57 hours (or 1 hour and 34 minutes) for the second jet to overtake the first.