SOLUTION: A and B run at constant velocities along a circular track. The circumference of the track is 1320 meters. If they run in opposite directions, they meet every 2 minutes; if they run

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A and B run at constant velocities along a circular track. The circumference of the track is 1320 meters. If they run in opposite directions, they meet every 2 minutes; if they run      Log On


   

Question 345476: A and B run at constant velocities along a circular track. The circumference of the track is 1320 meters. If they run in opposite directions, they meet every 2 minutes; if they run in the same direction, they are together every 22 minutes. Find their velocities.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A and B run at constant velocities along a circular track.
The circumference of the track is 1320 meters.
If they run in opposite directions, they meet every 2 minutes;
if they run in the same direction, they are together every 22 minutes.
Find their velocities.
:
Find the sum of their velocities,
when they meet, they will have traveled a total of 1320 meters in two minutes
Speed = dist/time
(V1 + V2) = 1320%2F2
V1 + V2 = 660 m/min
:
When they travel the same directions
V1 - V2 = 1320%2F22
V1 - V2 = 60 m/min
:
Use elimination
V1 + V2 = 660
V1 - V2 = 60
-----------------addition eliminates V2
2V1 = 720
V1 = 720%2F2
V1 = 360 m/sec
and
V2 = 660 - 360
V2 = 300 m/sec
:
:
We can confirm this using the same direction scenario
Faster runner travels 22 * 360 = 7920 meters
Slower runner travels 22 * 300 = 6600 meters
----------------------------------------------
difference is exactly 1 lap or 1320 meters