Question
At Kimberley station, a bus arrives every 20 minutes and a train arrives
every 18 minutes. The bus and train arrive at the same time at 12 pm .
After how many minutes will they both arrive at the same time again? (You
must assume that the buses and trains are always on time!)
every 18 minutes. The bus and train arrive at the same time at 12 pm .
After how many minutes will they both arrive at the same time again? (You
must assume that the buses and trains are always on time!)
Ask by Marsh Vaughn. in South Africa
Mar 17,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
They will both arrive at the same time again after 180 minutes.
Solution
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The Deep Dive
To figure out when the bus and train will arrive at the same time again, we need to find the least common multiple (LCM) of their arrival intervals. The bus comes every 20 minutes, and the train comes every 18 minutes.
The LCM of 20 and 18 can be found by breaking down each number into its prime factors:
20 = 2^2 * 5 and 18 = 2 * 3^2.
Taking the highest power of each prime, LCM = 2^2 * 3^2 * 5 = 4 * 9 * 5 = 180.
20 = 2^2 * 5 and 18 = 2 * 3^2.
Taking the highest power of each prime, LCM = 2^2 * 3^2 * 5 = 4 * 9 * 5 = 180.
Therefore, both the bus and train will arrive at the same time again after 180 minutes, which is 3 hours later, at 3:00 PM.
Happy traveling! 🚍🚆
