Exercise 36 Page 41

To calculate the distance traveled by each flight, we need to use the Distance Formula. It tells us that to find the distance traveled we need to multiply the rate

r

by the time

t .

d = r t

Let's divide the above formula by

r

to isolate

t .

d = r t \Leftrightarrow t = \frac{d}{r}

Let

d

be the distance traveled by each flight. The outbound flight averages

460

miles per hour and the return flight averages

500

miles per hour. Let's write an expression for the time taken in each flight.

Outbound Flight	Return Flight
$\frac{d}{4 6 0}$	$\frac{d}{5 0 0}$

The total flying time is the sum of the duration of both outbound and return flights. Moreover, we are told that the total flying time is

4.8

hours.

4.8 = \frac{d}{4 6 0} + \frac{d}{5 0 0}

Let's solve the above equation to find the value of

d .

4.8 = \frac{d}{4 6 0} + \frac{d}{5 0 0}

ExpandFrac

$\frac{a}{b} = \frac{a \cdot 5 0 0}{b \cdot 5 0 0}$

4.8 = \frac{d \cdot 5 0 0}{4 6 0 \cdot 5 0 0} + \frac{d}{5 0 0}

ExpandFrac

$\frac{a}{b} = \frac{a \cdot 4 6 0}{b \cdot 4 6 0}$

4.8 = \frac{d \cdot 5 0 0}{4 6 0 \cdot 5 0 0} + \frac{d \cdot 4 6 0}{5 0 0 \cdot 4 6 0}

Multiply

4.8 = \frac{5 0 0 d}{2 3 0 0 0 0} + \frac{4 6 0 d}{2 3 0 0 0 0}

AddFrac

Add fractions

4.8 = \frac{5 0 0 d + 4 6 0 d}{2 3 0 0 0 0}

AddTerms

Add terms

4.8 = \frac{9 6 0 d}{2 3 0 0 0 0}

MultEqn

$LHS \cdot 230000 = RHS \cdot 230000$

4.8 \cdot 230000 = 960 d

DivEqn

$LHS / 960 = RHS / 960$

\frac{4 . 8 \cdot 2 3 0 0 0 0}{9 6 0} = d

UseCalc

Use a calculator

1150 = d

RearrangeEqn

Rearrange equation

d = 1150

The distance traveled by each flight is

1150

miles.