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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?

Respuesta :

calculista

Answer:

7 times during the first 15 minutes

Step-by-step explanation:

Remember that

[tex]1\ min=60\ sec[/tex]

so

[tex]15\ min=15(60)=900\ sec[/tex]

Decompose the numbers 18 and 42 in prime factors

we know that

[tex]18=(2)(3^2)[/tex]

[tex]42=(2)(3)(7)[/tex]

Find the least common multiple (LCM)

The LCM is

[tex](2)(3^2)(7)=126\ sec[/tex]

we need to find all multiples of 126 that are less than or equal 900.

[tex]126*1=126\ sec\\126*2=252\ sec\\126*3=378\ sec\\126*4=504\ sec\\126*5=630\ sec\\126*6=756\ sec\\126*7=882\ sec[/tex]

therefore

7 times during the first 15 minutes

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