Rates 3

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Rates 3

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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) $minutes$ $\text(minutes)$

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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, fill up the quad boxes with the three known values and have the unknown value be

x

$x$ .

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

Next, equate the two columns and solve for

x

$x$ .

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

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

Since

x

$x$ is under the

min

$\text(min)$ column in the quad boxes, the value will be

8 minutes

$8 \text(minutes)$ .

8 minutes

$8 \text(minutes)$

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

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

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

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

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) $km$ $\text(km)$

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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

$60 \text(minutes)$

1 \times \frac{60}{1}

$1xx(60)/1$

=

$=$

60

$60$

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

x

$x$ .

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

Finally, equate the two columns and solve for

x

$x$ .

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

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

Since

x

$x$ is under the

km

$\text(km)$ column in the quad boxes, the value will be

340 kilometres

$340 \text(kilometres)$ .

340 km

$340 \text(km)$

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

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

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Quiz summary

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1. Question

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Correct!

2. Question

Hint

Well Done!

3. Question

Hint

Great Work!

4. Question

Hint

Excellent!

Speed-Distance-Time Formula

Quizzes

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

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