3 At a train station, the blue line has a train leaving every 15 minutes, the green line has a train leaving every 24 minutes and the red line every 10 minutes. If the first train on each line leaves at the same time.how often will there be trains on al three lines departing the train station at the same time ?
Answers
Given : At a train station, the blue line has a train leaving every 15 minutes, the green line has a train leaving every 24 minutes and the red line every 10 minutes. If the first train on each line leaves at the same time.
To Find : how often will there be trains on al three lines departing the train station at the same time
Solution:
Blue line every 15 mins
Green line every 24 mins
Red line every 10 mins
To Find time when trains will leave together ,
need to find LCM ( 15 , 24 , 10)
15 = 3 * 5
24 = 2 * 2 * 2 * 3
10 = 2 * 5
LCM = 2 * 2 * 2* 3 * 5
= 120
Every 120 mins = 2 Hrs trains will depart at the same time
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Step-by-step explanation:
Given:
At a train station, the blue line has a train leaving every 15 minutes, the green line has a train leaving every 24 minutes and the red line every 10 minutes.
To find:
How often will there be trains on al three lines departing the train station at the same time?
Solution:
Blue line in every = 15 Minutes
Green line in every = 24 Minutes
Red line in every = 10 Minutes
We have to find time when train will leave together:
So we need to find the L.C.M of 15, 24, 10.
Prime Factorisation of 15:
15 = 3 x 5
Prime Factorisation of 24:
24 = 2 x 2 x 2 x 3 x5
Prime Factorisation of 10:
10 = 5 x 2
Therefore, LCM = 2 x 2 x 2 x 3 x 5 = 120
Every 120 min = 2 Hours the train will depart.