Question

Three racing cars leave the starting line at the same time. The first car completes a lap every 175 seconds, the second car completes a lap every 126 seconds, and the third one every 90 seconds. (1) How long will it take for the three cars to meet at the starting line for the first time after the race begins?

Answer 1

To find out how long it will take for the three cars to meet at the starting line for the first time, we need to determine the least common multiple (LCM) of their lap times. The LCM of their lap times is 18375 seconds or approximately 5 hours and 6 minutes.

Step-by-step explanation:

To find out how long it will take for the three cars to meet at the starting line for the first time, we need to determine the least common multiple (LCM) of their lap times. The LCM of the lap times for the three cars can be calculated as follows:

LCM(175, 126, 90) = LCM(3, 5, 7) x 175

LCM(3, 5, 7) = 3 x 5 x 7 = 105

LCM(175, 126, 90) = 105 x 175 = 18375 seconds

Therefore, it will take 18375 seconds or approximately 5 hours and 6 minutes for the three cars to meet at the starting line for the first time after the race begins.

The LCM of their lap times is 18375 seconds or approximately 5 hours and 6 minutes.