Question

A cell phone tower has a safety light to warn airplanes of its location. It blinks once every 3.5 seconds. If $ f(m) $ gives the number of times the light blinks over the course of m minutes, which of the following equations defines $ f $
(A) $ f(m) = 2.5m $
(B) $ f(m) = \dfrac{{3.5m}}{{60}} $
(C) $ f(m) = \dfrac{{60m}}{{3.5}} $
(D) $ f(m) = 210m $

Answer 1

Hint: Use the fact: 1 minute = 60 seconds or 1 second = $ \dfrac{1}{{60}} $ minutes. Convert 3.5 seconds into minutes. Compute the number of blinks in 1 minute. Multiply the answer by m to get the function.

Complete step-by-step answer:
We have a cell phone tower which has a safety light that blinks once every 3.5 seconds.
We are given the function $ f(m) = $ number of times the light blinks over the course of m minutes.
We need to determine the definition of $ f(m) $ from the given options.
As $ f(m) $ is the count of blinks over the course of m minutes, we need to convert all the other information in terms of minutes.
1 minute = 60 seconds $ \Rightarrow $ 1 second = $ \dfrac{1}{{60}} $ minutes
Therefore 3.5 seconds = $ \dfrac{1}{{60}} \times 3.5 = \dfrac{{3.5}}{{60}} $ minutes.
This means that the safety light blinks once every $ \dfrac{{3.5}}{{60}} $ minutes.
1 blink = $ \dfrac{{3.5}}{{60}} $ minutes
Dividing $ \dfrac{{3.5}}{{60}} $ on both the sides, we get
 $ \dfrac{1}{{\dfrac{{3.5}}{{60}}}} $ blink =\[\dfrac{{\dfrac{{3.5}}{{60}}}}{{\dfrac{{3.5}}{{60}}}}\]minutes
 $ \Rightarrow \dfrac{{60}}{{3.5}} $ blink = 1 minute
or 1 minute = $ \dfrac{{60}}{{3.5}} $ blink… (1)
Therefore, over the course of m minutes, the count of blinks will be obtained as follows:
Multiply m on both sides of the equation (1).
Thus, we have $ (1 \times m) $ minutes = $ \dfrac{{60}}{{3.5}} \times m $ blinks = $ \dfrac{{60m}}{{3.5}} $ blinks.
Hence, we can define $ f(m) $ as $ f(m) = \dfrac{{60m}}{{3.5}} $
So, the correct answer is “Option C”.

Note: Do not convert minutes into seconds in this problem. Because it will affect the function which is defined over the course of minutes as the problem demands that to find the number of time light blinks in a complete minute.