Lesson Flying back and forth

Flying back and forth

Problem 1

Joe and Frank approach each other at the rate 6+6 = 12 miles per hour.


Hence, they will meet each other in 36/12 = 3 hours.


During these 3 hours, flying at the rate of 18 miles per hour, the pigeon will cover the distance of 3*18 = 54 miles.   ANSWER

Problem 2

 
(a)  Question (a) is simple. Initial distance is 150 meters and the rate of approaching is

     3 + 5 = 8 m/s.  So, the time till the first meeting is  150/8 = 18.75 seconds.    ANSWER


     At this point, part (a) is complete.



(b)  Faster bee covers 150 m in  150/5 = 30 seconds, and after that changes the direction to opposite.

     Slover bee covers 150 m in  150/3 = 50 seconds.


     So, when the faster bee completes 150 m in 30 seconds, the slower bee is still on the way to its turning point,

     and the slower bee will fly additional 50-30 = 20 seconds to get its turning point.


     During these 20 seconds, the faster bee, which just changed its direction to opposite,
     will cover 20*5 = 100 meters.


     So, when the slower bee will reach its turning point, the distance between the bees will be 150 - 100 = 50 m.


     Now both bees fly towards each other at the approaching rate of 3+5 = 8 m/s (again).

     So, they will cover  50 m  in 50/8 = 6.25 seconds.



     Thus, the time to meet for the second time is 30 + 20 + 6.25 = 56.25 seconds (counting from the start).    ANSWER


     It is the same as to say that they will meet in the second time 56.25 - 18.75 = 37.5 seconds after their first meeting moment.