Question

a certain flock of birds will travel m miles in total without stopping at an average velocity of v mph. which of the following equations models the number of days, d, that the birds will fly without stopping?
a. d = \frac{m}{60v}
b. d = \frac{60m}{v}
c. d = \frac{24m}{v}
d. d = \frac{m}{24v}

Explanation:

Step1: Recall the formula for time

The formula for time \(t=\frac{d}{v}\) (where \(d\) is distance, \(v\) is velocity). We want to find the number of days \(d\). First, convert the total distance \(m\) miles and velocity \(v\) mph into days.

Step2: Calculate the number of hours in a day

There are \(24\) hours in a day. The time \(t\) (in hours) to cover \(m\) miles at a speed of \(v\) mph is \(t = \frac{m}{v}\) (from \(t=\frac{d}{v}\), here \(d = m\)).

Step3: Convert hours to days

Since there are \(24\) hours in a day, the number of days \(d=\frac{\frac{m}{v}}{24}\).

Step4: Simplify the expression

Using the rule of dividing fractions \(\frac{a}{b}\div c=\frac{a}{b\times c}\), we get \(d=\frac{m}{24v}\).

Answer:

D. \(d = \frac{m}{24v}\)