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Big Ideas Math Algebra 2, 2014

BI

Big Ideas Math Algebra 2, 2014 View details

Cumulative Assessment

Exercise 3 Page 290

Practice makes perfect

a By substituting the number of people into the formula, we can calculate the speed of the boat. Note that we need a calculator for this.

rowers	$4.62 9 n$	$s$
$n = 2$	$4.6292$	$\approx 5.0$
$n = 4$	$4.6294$	$\approx 5.4$
$n = 8$	$4.6298$	$\approx 5.8$

b If we call the smaller number of people

n = P,

then twice this number can be expressed as

n = 2 P .

With this, we can write two expressions for the speed of the boat when it holds the different number of rowers.

P rowers : 2P rowers : s_{P} = 4.62 9 P s_{2 P} = 4.62 9 2 P

To compare the different speeds, we divide the expression for the speed of the boat with the greater number of rowers, with the expression for the speed of the boat with the lower number of rowers. The quotient will tell us how many times the speed increases when the rowers double.

\frac{S _{2 P}}{S _{P}}

$S_{2 P} = 4.62 9 2 P$ , $S_{P} = 4.62 9 P$

\frac{4 . 6 2 9 2 P}{4 . 6 2 9 P}

▼

Simplify

$a \cdot b = a \cdot b$

\frac{4 . 6 2 9 2 9 P}{4 . 6 2 9 P}

$\frac{a}{b} = \frac{a / 4 . 6 2 9 P}{b / 4 . 6 2 9 P}$

92

Use a calculator

1.08006 \dots

Round to $2$ decimal place(s)

\approx 1.08

The boat with twice the number of rowers goes about

8 %

faster than the less crowded boat.

c From Part A, we know the speed that the boat travels when it has the different number of rowers.

2 rowers : 4 rowers : 8 rowers : s = 5.0 mps s \approx 5.4 mps s \approx 5.8 mps

By dividing the length of the race by these speeds, we can find the time it takes for each boat to complete it

rowers	speed	$\frac{2 0 0 0}{s}$	time
$2$	$s = 5$	$\frac{2 0 0 0}{5}$	$400 s$
$4$	$s \approx 5.4$	$\frac{2 0 0 0}{5 . 4}$	$\approx 370 s$
$8$	$s \approx 5.8$	$\frac{2 0 0 0}{5 . 8}$	$\approx 344 s$

Subchapter links

Exercises p.290-291