Two cars race around a circular track, in opposite directions, at constant rates. They start at the same point and meet every 30 seconds. If they move in the same direction, they meet every 120 seconds. If the track is 1800 metres long, what is the speed of each car?
Hint
1)
Let x = rate of car 1 (m/s)
Let y = rate of car 2 (m/s)
1800m = 30x+30y
1800-30x = 30y
2)
Use method of substitution or elimination.
Answer
Let x = rate of car 1 (m/s)
Let y = rate of car 2 (m/s)
(1) 1800m = 30x+30y
1800-30x = 30y
7200-120x = 120y
(2) 1800 + 120x = 120y
Solve for Car 1: (1)=(2)
7200-120x = 1800+120x
5400 = 240x
x = 22.5 m/s
Convert to km/hr
x = 22.5m/sec 60sec/min60min/hr = 81 km/hr
1000 m/km
Solve for Car 2:
Substitute x = 22.5 m/s
1800+120x = 120y
y = 1800+120x
120
y = 1800+120(22.5)
120
y = 37.5 m/s
Convert to km/hr
x =37.5m/sec 60sec/min60min/hr = 135 km/hr
1000 m/km