If aircraft A took of at 10am flying at 170 mph and aircraft B took of at 10.45am flying at 230 mph. When would they meet and how far would they have travelled?
Va (Speed of Aircraft A) = 170 mph
Vb (Speed of Aircraft B) = 230 mph
Departure time of A: 10:00
Departure time of A: 10:45
45 minutes = 0.75 hours
After 45 minutes Distance travelled by Aircraft A: D = Va x 45 minutes = 170 x 0.75 =
127.5 miles
Now calculate relative speed of aircraft B: V =
Vb - Va = 230 - 170 =
60 mph
Now calculate time taken for Aircraft B to catch up. ie time taken for Aircraft B to travel 127.5 miles at 60 mph: T = 127.5 / 60 =
2.125 hours
Now calculate total distance Aircraft A has travelled: Da = 170 x 2.875 (2.125 + 0.75) =
488.75 miles
Total distance Aircraft B has travelled: Db = 230 x 2.125 =
488.75 miles
Therefore,
total distance
both aircraft have now travelled: 488.75 + 488.75 =
977.5 miles
Time taken to meet: T = Db /
Vb = 488.75 / 230 =
2.125 hours after Aircraft
B departs.
This is equivalent of
127.5 minutes (2.125 x 60). So 10:45 + 127.5 minutes =
12:52:30 (12:52pm and 30 seconds).
Or
T = Da / Va = 488.75 / 170 =
2.875 hours after Aircraft
A departs. 10:00 + 172.5 =
12:52:30