I am having trouble explain this problem to my daughter. Thisis the problem. If

Question

I am having trouble explain this problem to my daughter. Thisis the problem. If 3 bells ring @ intervals of 40, 36, 24 minutesrespectively. At what time will they ring together again if theystart simultaneously at 12 noon. How many times will each bell ringduring that time? I am having trouble explain this problem to my daughter. Thisis the problem. If 3 bells ring @ intervals of 40, 36, 24 minutesrespectively. At what time will they ring together again if theystart simultaneously at 12 noon. How many times will each bell ringduring that time?

Explanation / Answer

Let bell 1 be x: x rings every 40 minutes: 1200, 1240,120 / 200, 240, 320 / 400, 440, 520 / 600, etc .... the point isthat after 3 rings, the process repeats at the top of every 2ndhour. Let bell 2 be y: y rings every 36 minutes: 1200, 1236, 112,148, 224 / 300, 336, 412, 448, 524 / 600, etc ... the point is thatafter 5 rings, the process repeats at the top of every 3rdhour. Let bell 3 be z: z rings every 24 minutes: 1200, 1224, 1248, 112,136 / 200, 224, 248, 312, 336 / 400, 424, 228, 512, 536 / 600 ...the point is that after 5 rings, the process repeats itself at thetop of every 2nd hour, as well. that means x hits the top of the hour evenly at 1200, 200, 400,600, etc y hits at the top of the hours evenly at 1200, 300, 600, 900,etc and x hits at the top of the hours evenly at 1200, 200, 400, 600,etc... The answer is 6 p.m. is the next time all three of these bells willrings simultaneously.

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