Rob can complete his bus route in 6 hours. Joan can complete her bus route in 3 hours. If they left the terminal at 3:00 am and after each completed route returned to the terminal, determine the next time they would leave the terminal at the same time.
Please explain how to compute to arrive at the answer and I will find the answer myself.
THANKS
To determine the next time Rob and Joan would leave the terminal at the same time, we need to find the least common multiple (LCM) of their individual times.
The LCM is the smallest multiple that both numbers share. To find the LCM of two numbers, we can use the following steps:
1. Find the greatest common divisor (GCD) of the two numbers. The GCD is the largest number that divides both of the given numbers without leaving a remainder.
2. Divide one of the numbers by the GCD.
3. Multiply the result from step 2 by the other number.
Let's calculate the LCM for Rob and Joan's times:
Rob's time = 6 hours
Joan's time = 3 hours
1. To determine the GCD of 6 and 3, we can use the Euclidean algorithm:
- Divide 6 by 3: 6 ÷ 3 = 2 with no remainder.
- Therefore, the GCD of 6 and 3 is 3.
2. Divide one of the numbers (6) by the GCD (3):
6 ÷ 3 = 2
3. Multiply the result (2) by the other number (3):
2 × 3 = 6
So, the LCM of 6 and 3 is 6.
This means that the next time Rob and Joan would leave the terminal at the same time is after 6 hours.
To find the specific time, we need to add the 6 hours to the initial departure time, which was 3:00 am.
Adding 6 hours to 3:00 am, we get the answer:
3:00 am + 6 hours = 9:00 am
Therefore, the next time Rob and Joan would leave the terminal at the same time is 9:00 am.