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Question 1 of 4

A factory produces

250

$250$ cans within a minute. How long will it take to make

2000

$2000$ cans?

(8) $minutes$ $\text(minutes)$

Question 2 of 4

2. Question
A factory produces $250$ $250$ cans within a minute. How many cans can they produce in an $8$ $8$ -hour shift?
- (120000) $cans$ $\text(cans)$
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A rate is a ratio of two different units.

Quad boxes are used to easily find rates
(Use cross product method)

First, convert the hours into minutes

$1 hour$ $1 \text(hour)$ $=$ $=$ $60 minutes$ $60 \text(minutes)$

$8 \times \frac{60}{1}$ $8xx(60)/1$ $=$ $=$ $480$ $480$

Next, fill up the quad boxes with the three known values and have the unknown value be $x$ $x$ .

Cans Min

$250$ $250$ $1$ $1$

$x$ $x$ $480$ $480$

Finally, equate the two columns and solve for $x$ $x$ .

$\frac{250}{x}$ $(250)/x$ $=$ $=$ $\frac{1}{480}$ $1/(480)$

$1 (x)$ $1(x)$ $=$ $=$ $250 (480)$ $250(480)$ Cross multiply

$x$ $x$ $=$ $=$ $120000$ $120 000$

Since $x$ $x$ is under the $cans$ $\text(cans)$ column in the quad boxes, the value will be $120000 cans$ $120 000 \text(cans)$ .

$120000 cans$ $120 000 \text(cans)$

Cans	Min
$250$ $250$	$1$ $1$
$2000$ $2000$	$x$ $x$

Cans	Min
$250$ $250$	$1$ $1$
$x$ $x$	$480$ $480$

Question 3 of 4

A jet flies at a speed of

680 km/hour

$680 \text(km/hour)$ . How far can it travel within

30

$30$ minutes?

(340) $km$ $\text(km)$

km	Min
$680$ $680$	$60$ $60$
$x$ $x$	$30$ $30$

Question 4 of 4

A man has been driving at

70 km/hour

$70 \text(km/hour)$ for

9

$9$ hours. How far did he travel?

(630) $km$ $\text(km)$

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Speed-Distance-Time Formula

Speed = \frac{Distance}{Time}

$\color{#00880a}{\text{Speed}}=\frac{\color{#9a00c7}{\text{Distance}}}{\color{#e65021}{\text{Time}}}$

First, derive the formula to solve for the distance.

$\color{#00880a}{\text{Speed}}$	$=$ $=$	$\frac{\color{#9a00c7}{\text{Distance}}}{\color{#e65021}{\text{Time}}}$

$\color{#9a00c7}{\text{Distance}}$	$=$ $=$	$\color{#00880a}{\text{Speed}}\cdot\color{#e65021}{\text{Time}}$	Cross multiply

Next, substitute the known values to the derived formula.

$Speed$ $\text(Speed)$	$=$ $=$	$\frac{70 km}{hour}$ $(70 \text(km))/(\text(hour))$

$Time$ $\text(Time)$	$=$ $=$	$9 hours$ $9 \text(hours)$

$\color{#9a00c7}{\text{Distance}}$	$=$ $=$	$\color{#00880a}{\text{Speed}}\cdot\color{#e65021}{\text{Time}}$

	$=$ $=$	$\color{#00880a}{\frac{70\;\text{km}}{\text{hour}}}\cdot\color{#e65021}{9\text{hours}}$	Substitute known values

	$=$ $=$	$630 km$ $630 \text(km)$	Hours cancel out

Distance = 630 km

$\text(Distance)=630 \text(km)$

$\frac{680}{x}$ $(680)/x$	$=$ $=$	$\frac{60}{30}$ $(60)/(30)$

$60 (x)$ $60(x)$	$=$ $=$	$680 (30)$ $680(30)$	Cross multiply
$60 x$ $60x$ $\div 60$ $divide60$	$=$ $=$	$20400$ $20 400$ $\div 60$ $divide60$	Divide both sides by $60$ $60$
$x$ $x$	$=$ $=$	$340$ $340$

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Speed-Distance-Time Formula

Quizzes

$\frac{250}{2000}$ $(250)/(2000)$	$=$ $=$	$\frac{1}{x}$ $1/x$

$250 (x)$ $250(x)$	$=$ $=$	$1 (2000)$ $1(2000)$	Cross multiply
$250 x$ $250x$ $\div 250$ $divide250$	$=$ $=$	$2000$ $2000$ $\div 250$ $divide250$	Divide both sides by $250$ $250$
$x$ $x$	$=$ $=$	$8$ $8$

$\frac{250}{x}$ $(250)/x$	$=$ $=$	$\frac{1}{480}$ $1/(480)$

$1 (x)$ $1(x)$	$=$ $=$	$250 (480)$ $250(480)$	Cross multiply
$x$ $x$	$=$ $=$	$120000$ $120 000$