Exercise 29 Page 731

Practice makes perfect

a We know the speed of the wind

w,

the speed set by the pilot

r,

and the total speed

s .

Now we will write two equations.

An equation for the total speed with a headwind.
An equation for the total speed with a tailwind.

Equation With a Headwind

We know headwinds decrease the total speed of the plane. Therefore, to write an equation of the

total speed

of the plane we will subtract the

speed of the headwind

from the

pilot ’ s speed .

Total Speed = Pilot Speed - Headwind Speed ⇓ s = r - w

Equation With a Tailwind

We are told that tailwinds increase the total speed of the plane. Therefore, when writing an equation of the

total speed

of the plane, we will add the

speed of the tailwind

to the

pilot ’ s speed .

Total Speed = Pilot Speed + Tailwind Speed ⇓ s = r + w

b In this exercise we will write equations for the distance traveled and we will solve these equations for

t .

Distance Traveled With a Headwind

We found the total speed of the plane with a headwind in Part A. We will use this information to write the equation for the distance traveled. We will write the equation by using the distance formula, in which we will represent the distance traveled as

d

and the time as

t .

Distance = Total Speed \cdot Time ⇓ d = (r - w) (t)

Now we will solve this equation for

t .

d = (r - w) (t)

DivEqn

$LHS / (r - w) = RHS / (r - w)$

\frac{d}{r - w} = t

RearrangeEqn

Rearrange equation

t = \frac{d}{r - w}

Distance Traveled With a Tailwind

To write the equation for the distance traveled we will use the equation for the total speed of the plane with the tailwind that we found in Part A. We will proceed the same way as the equation for the distance traveled with the headwind.

Distance = Total Speed \cdot Time ⇓ d = (r + w) (t)

Now we will solve this equation for

t .

d = (r + w) (t)

DivEqn

$LHS / (r + w) = RHS / (r + w)$

\frac{d}{r + w} = t

RearrangeEqn

Rearrange equation

t = \frac{d}{r + w}

Subchapter links

Check Your Understanding p.730

H.O.T. Problems p.731

Standardized Test Practice p.732

Spiral Review p.732

Skills Review p.732

Exercise 29 Page 731

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Practice exercises

Asses your skill

Equation With a Headwind

Equation With a Tailwind

Distance Traveled With a Headwind

Distance Traveled With a Tailwind