Chapter 8.5, Problem 22PPS

a.

To determine

To write a direct variation equation.

Answer to Problem 22PPS

The equation is related as $d=50t$

Explanation of Solution

Given information:

A group of snow geese migrated 375 miles in 7.5 hours.

Write a direct variation equation that represents this situation.

The equation can be obtained as

  $\begin{array}{l}d\propto t\\ d=kt\left[\begin{array}{l}d\text{=distance}\\ t=\text{time}\\ k=\text{constant}\end{array}\right]\end{array}$

Put the values of $d=375\text{ and }t=\text{7}\text{.5 in above equation}$

  $\begin{array}{l}378=7.5*k\\ k=\frac{375}{7.5}\\ k=50\left[\text{divide numerator and denominator by 7}\text{.5}\right]\end{array}$

Hence,

The equation is related as $d=50t$

b.

To determine

To find the number of hours of flying time.

Answer to Problem 22PPS

The value of $t\text{ is 3}\text{.2 hours}$

Explanation of Solution

Given information:

Every year, geese migrate 3000 miles from their winter home in the southwest United States to their summer home in the Canadian Arctic. Estimate the number of hours of flying time that it take for the geese to migrate.

Calculation:

The time can be obtained as.

Since we find out $d=50t$ in previous part

Put $d=3000\left[d\text{=distances}\right]$

Therefore

  $\begin{array}{l}3000=50t\\ t=\frac{3000}{50}\\ t=60\text{ hours }\left[\text{divide numerator and denominator by 50}\right]\end{array}$

Hence,

The value of $t\text{ is 60 hours}$