<PRE><B>Question 156483</B>
2 cars race around a circular track, in opposite directions, at constant speeds.
 They start at the same point and meet every 30.0 seconds. If they move in the
 same direction, they meet every 120.0 seconds. If the track is 1800 meters
 long, what is the speed of each car?
:
Change seconds to min in the problem
:
Let a = speed of car a (in meters/min)
Let b = speed of car b
:
.5(a+b) = 1800
Multiply equation by 2
a + b = 3600
:
2(a-b) = 1800
Divide both sides by 2
a - b = 900
:
a + b = 3600
a - b = 900
--------------adding eliminates b
2a = 4500
a = {{{4500/2}}}
a = 2250 meters/min ({{{(2250*60)/1000}}} = 135 km/hr)
:
Find the speed of b
a + b = 3600
a + 2250 = 3600
a = 3600 - 2250
a = 1350 meters/min ({{{(1350*60)/1000}}} = 81 km/hr)</PRE>