Two trains arrived at a station at 2:55 P.M., with one arriving on Track A, and the other arriving on Track B. Trains arrive on Track A every 16 minutes, and they arrive on Track B every 18 minutes. At what time will trains next arrive at the same time on both tracks?
A) 4:07 P.M.
B) 5:19 P.M.
C) 6:31 P.M.
D) 7:43 P.M.
LCM(16,18) = 144 or 2:24
2:55 PM + 2:24 = 5:19 PM
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To solve this problem, we need to find the least common multiple (LCM) of the two arrival times.
The arrival time for trains on Track A is every 16 minutes.
The arrival time for trains on Track B is every 18 minutes.
To find the LCM, we can use prime factorization.
Prime factorization of 16: 2 * 2 * 2 * 2
Prime factorization of 18: 2 * 3 * 3
Now we consider the highest power for each prime factor:
2 (four times) and 3 (two times).
Multiplying the highest powers:
2^4 * 3^2 = 16 * 9 = 144
Therefore, the LCM of 16 and 18 is 144 minutes.
Now, let's calculate the time at which the next trains will arrive at the same time on both tracks.
The two trains arrived at the station at 2:55 P.M.
Adding 144 minutes to the current time:
2:55 P.M. + 144 minutes = 4:59 P.M.
Therefore, the next time the trains will arrive at the same time on both tracks is 4:59 P.M.
Option A) 4:07 P.M. is not the correct answer because it is earlier than the calculated time.
Option B) 5:19 P.M. is not the correct answer because it is later than the calculated time.
Option C) 6:31 P.M. is not the correct answer because it is even later than option B.
Option D) 7:43 P.M. is not the correct answer because it is even later than option C.
The correct answer is 4:59 P.M.