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
Answer:
30
Step-by-step explanation:
whenever 15x = 24y =10z where x,y,z are integers and
15x < 3600
24y < 3600
10z < 3600
so take factors of 15,24,10 upto 3600
so y = 5,10,15...upto 150
so 150 = 5 + (n-1) 5
n = 30
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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