Hi, Gin,
I'll assume that both bees (B1 and B2) leave on the opposite sides of the 210 meter distance and head towards each other.
AB (=210 meters)
This means that once the bees have traveled a CUMULATIVE distance of 210 meters, they meet.
B1 speed = 3 m/s, and
B2 speed = 7 m/s
Technically, one of these speeds should be a negative, since it is going from right to left. But what's important now is calculate the total distance covered.
We know that time(t) x speed = distance. The total distance traveled by both bees is:
B1 = 3m/s * t
B2 = 7m/s * t
For a time, t, the total distance(D) traveled is
D =3m/s *t + 7m/s *t, or
210 meters = 10m/s * t
t = 21 seconds
Check:
Distance traveled by each bee in 21 seconds:
B1 = 21s*3m/2 = 63 meters
B2 = 21s * 7m/s = 147 meters
Total = 210 meters.
Imagine a straight line AB with starting coordinates of (0,0) for B1 and (210, 0)
Assume B1 moves to the right (start at (0,0). At 21 seconds it is at point (63,0). Since B1 moves left, it moves a negative 147 meters in 21 seconds (210 - 147), which also places it at (63,0).
If the bees keep going, they'll never meet again. Assuming they keep going and immediately reverse direction at each other's starting point, they would have to travel another 210 meters. That would add another 21 seconds for a total of 42 seconds. A that point, one will exclaim "we can't keep meeting like this."
Bob
