Pamela and David walk on the same track. It tqkes Pamela 9 minutes and David 6 minutes to walk one lap.If they start walking at the same time, how many laps will each have walked when they cross the starting point together for the first time?
At 18 min, one has went around twice, and the other three times. How did I know that?
To find out how many laps Pamela and David will have walked when they cross the starting point together for the first time, we need to determine the least common multiple (LCM) of their lap times.
First, let's find the LCM of 9 minutes and 6 minutes:
Multiples of 9 minutes: 9, 18, 27, 36, 45, 54, 63...
Multiples of 6 minutes: 6, 12, 18, 24, 30, 36, 42, 48, 54...
The first common multiple is 18 minutes. Therefore, they will both be back at the starting point after 18 minutes.
Next, let's calculate the number of laps they would have walked in 18 minutes:
Pamela: Since it takes Pamela 9 minutes to walk one lap, in 18 minutes, she will have walked 18/9 = 2 laps.
David: Similarly, since it takes David 6 minutes to walk one lap, in 18 minutes, he will have walked 18/6 = 3 laps.
Therefore, Pamela would have walked 2 laps and David would have walked 3 laps when they cross the starting point together for the first time.