Hello, I need help with a 5th grade math question. The red train returns to central station every 45 min. The blue train returns to central station every 60 min. If both trains leave the station together, in how many min. will they both be back at the station at the same time?
Assume that both trains are at the stations now, then they will be back again at the following times
red train: 45 90 135 180 225 270 315 .. minutes from now
blue train: 60 120 180 240 300 360 ... minutes from now
What do you think?
the answer is so easy and what grade are you in
360
380
To find out when both trains will be back at the station at the same time, we need to find the least common multiple (LCM) of 45 and 60. The LCM is the smallest multiple that both numbers share.
To find the LCM, we can use either prime factorization or the method of listing multiples. Let's use listing multiples in this case:
For the red train:
Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360, ...
For the blue train:
Multiples of 60: 60, 120, 180, 240, 300, 360, ...
From the lists, we can see that the least common multiple of 45 and 60 is 180. Therefore, both trains will be back at the station at the same time in 180 minutes.