Two race cars are speeding around the racetrack at different speeds. One goes around the track in 2 minutes; the other goes around the track in 11/2 minutes. How often does the faster car pass the slower car?
3 1/2
Every six minutes. Six is the LCM (lowest common multiple) of 2 and 1.5.
To determine how often the faster car passes the slower car, we need to find the number of laps completed by each car during the given time period.
First, let's find the number of laps completed by the slower car in 2 minutes:
Number of laps = Time / Lap Time = 2 minutes / 1.5 minutes per lap = 4/3 laps
Next, let's find the number of laps completed by the faster car in 2 minutes:
Number of laps = Time / Lap Time = 2 minutes / 2 minutes per lap = 1 lap
Since the faster car completes only 1 lap in 2 minutes, it will pass the slower car once.
Therefore, the faster car passes the slower car once during the given time period.
To determine how often the faster car passes the slower car, we need to find out how many laps the faster car completes while the slower car completes one lap.
First, let's calculate the number of laps the slower car completes in 2 minutes. Since the slower car takes 11/2 minutes (or 1.5 minutes) to complete one lap, we can divide 2 minutes by 1.5 minutes to find the number of laps:
2 minutes / 1.5 minutes = 1.33 laps
Since we cannot have a fraction of a lap, we round down to the nearest whole number. Therefore, the slower car completes 1 lap in 2 minutes.
Now that we know the slower car completes 1 lap in 2 minutes, we can calculate how many laps the faster car completes in that time. Since the faster car goes around the track in 2 minutes, it also completes 1 lap in that time.
Therefore, the faster car passes the slower car once every lap.