Question

At the Earlington Heights station on the Miami Dade Metrorail, an orange line train arrives every 14 minutes, and a green line train arrives every 8 minutes. If a train from each line arrives at 7:00 AM, at what time will trains from both lines next arrive simultaneously?

Answer 1

The next time that the trains from both lines will arrive simultaneously, using their least common multiple, is 7:56 A.M.

What is the least common multiple?

The least common multiple (LCM) is the smallest number of a multiple of two or more numbers.

For instance, the LCM of 8 and 14 is 56.  The LCM shows that in 56 minutes from 7:00 A.M., the orange line must have arrived 4 times (14 x 4 = 56), while the green line must have arrived 7 times (8 x 7 = 56).

Data and Calculations:

                    Orange Line   Green Line

Arrival Time  14 minutes       8 minutes

The time that they arrive together is 7:00 A.M.

The least common factor of 14 and 8 is 56 because

8 = 2 × 2 × 2

14 = 2 × 7

LCM (8, 14) = 2 × 2 × 2 × 7 = 56

The number of times that the Orange Line will arrive in 56 minutes, taking 14 minutes per arrival is 4 times (56/14).

The number of times that the Green Line will arrive in 56 minutes, taking 8 minutes per arrival is 7 times (56/8).

Thus, the next time that the trains from both lines will arrive simultaneously is 7:56 A.M (7:00 A.M. + 56 minutes).

Learn more about the Least Common Multiple at brainly.com/question/16054958

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