Distance problem involving bees flying at each other at varying speeds.

Question

Two bees leave two locations 150 meters apart and fly, without stopping, back and forth between these two locations at average speeds of 3 meters per second and 5 meters per second, respectively. How long is it until the bees meet for the first time? How long is it until they meet for the second time?

Answer 1

For the first meeting

 

3t + 5t = 150

8t = 150

t = 18.75

 

The bees meet after 18.75 seconds.

 

For the second meeting

 

The slow bee has flown 56.25 meters. He has 93.75 meters to the other location.

The fast bee has flown 93.75 meters. He has 56.25 meters to the other location.

 

3t + 5t = 150 + 93.75 + 56.25 

8t = 300

8t = 150

t = 37.5

 

The second meeting occurs 37.5 seconds later.