Chapter 7, Problem 39CR

To determine

To findthe airspeeds of planes.

Answer to Problem 39CR

Speeds of planes are $\begin{array}{l}916.6miles/hourand856.6miles/hour.\hfill \\ \hfill \end{array}$

Explanation of Solution

Given Information: Given that two planes leave at the same time, one plane flies 60 miles per hour faster than other. Cities are 257 miles apart planes pass each other after 30 minutes of flying time.

Planes pass each other at 30 minutes of flying time.

Then ${\text{v}}_{\text{1}}{\text{ + v}}_{\text{2}}\text{ = }\frac{\text{257}}{\text{0}\text{.3}}\text{ miles/hour(i)}$

One plane fly 60 miles per hour faster

  ${\text{v}}_2{\text{ - v}}_1\text{ = 60 miles/hour(ii)}$

Adding equations (i) and (ii)

  $2v_2=\frac{2570}{3}+\frac{60}{1}$

  $\begin{array}{l}=\frac{2570+180}{3}\\ =\frac{2750}{3}\\ =\text{916}\text{.6 miles/hour}\end{array}$

Speed of other plane is 60 miles less

Then $v_1=916.6-60$

  $=\text{856}\text{.6 miles/hour}$