Question

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?

Answer 1

60 seconds make up a minute, The problem says `How many times during the first 15 minutes` meaning that we are going to have to do \(15min=15*60=900seconds\).

Answer 2

Now we have to find the LCM (Least Common Multiple)
\(\Bbb 18=(2)(3^2)\)
\(\Bbb 42=(2)(3)(7)\)
\((2)(3^2)(7)=?\)
\[(2)(9)(7)=\]\[(18)(7)=\]\(\large\sf 126\ seconds\)

Answer 3

That's not the answer though.
We have to find the common multiples of both 18 and 42, and they have to be ≤900
So, we are finding all the multiples of 126 that are \(≤900\), the way we do it is,
\(\sf 126(1)=126\ seconds\)
\(\sf 126(2)=252\ seconds\)
\(\sf 126(3)=378\ seconds\)
And so on until you get to the closest thing to 900 without going over it.
Or it can be equal to 900 but it can't because nothing multiplied by 126 will give you 900.

Answer 4

Now, to get your answer, you will have to count how many numbers there were that were less than 900 from when we were multiplying above, I did three of them as an example, now you have to do the rest until it gets the closest it can to 900 without going over it and then count how much numbers are after your equal signs, all of the factors, and don't add them up, just count how much you have and that will be your answer.