Mr. Rr the Rreliable Rrobot has been programmed to whistle every $18$ seconds and do a jumping jack every $42$ seconds, starting from the moment he is turned on. (For example, he does his first jumping jack $42$ seconds after he is turned on.)

How many times during the first $15$ minutes after activation will Mr. Rr whistle and do a jumping jack at the same instant?

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Mathematics

29 August, 07:49

Mr. Rr the Rreliable Rrobot has been programmed to whistle every $18$ seconds and do a jumping jack every $42$ seconds, starting from the moment he is turned on. (For example, he does his first jumping jack $42$ seconds after he is turned on.)

How many times during the first $15$ minutes after activation will Mr. Rr whistle and do a jumping jack at the same instant?

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Answers (1)

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Damon Paul · Answer 1

We need to know the the least common multiple ...

15=3*5, 42=2*3*7

LCM=2*3*5*7=210

There are 15*60=900 seconds in fifteen minutes. And we know that simultaneous whistling/jumping only occurs on multiples of 210 seconds ...

0≤210n≤900

0/210≤n≤30/7 since n must be an integer ...

1≤n≤4

So the number of times that this occurs is 4-1+1=4 times in the first fifteen minutes.