Rates 3

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Rates 3

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Question 1 of 4

1. Question
A factory produces $250$ $250$ cans within a minute. How long will it take to make $2000$ cans?
- (8) $\text(minutes)$
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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 $x$ .

Cans Min

$250$ $1$

$2000$ $x$

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

$(250)/(2000)$ $=$ $1/x$

$250(x)$ $=$ $1(2000)$ Cross multiply

$250x$ $divide250$ $=$ $2000$ $divide250$ Divide both sides by $250$

$x$ $=$ $8$

Since $x$ is under the $\text(min)$ column in the quad boxes, the value will be $8 \text(minutes)$ .

$8 \text(minutes)$
Question 2 of 4

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

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

$8xx(60)/1$ $=$ $480$

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

Cans Min

$250$ $1$

$x$ $480$

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

$(250)/x$ $=$ $1/(480)$

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

$x$ $=$ $120 000$

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

$120 000 \text(cans)$
Question 3 of 4

3. Question
A jet flies at a speed of $680 \text(km/hour)$ . How far can it travel within $30$ minutes?
- (340) $\text(km)$
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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

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

$1xx(60)/1$ $=$ $60$

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

km Min

$680$ $60$

$x$ $30$

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

$(680)/x$ $=$ $(60)/(30)$

$60(x)$ $=$ $680(30)$ Cross multiply

$60x$ $divide60$ $=$ $20 400$ $divide60$ Divide both sides by $60$

$x$ $=$ $340$

Since $x$ is under the $\text(km)$ column in the quad boxes, the value will be $340 \text(kilometres)$ .

$340 \text(km)$

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

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

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

Question 4 of 4

A man has been driving at

$70 \text(km/hour)$ for

$9$ hours. How far did he travel?

(630) $\text(km)$

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Speed-Distance-Time Formula

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

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.

$\text(Speed)$	$=$	$(70 \text(km))/(\text(hour))$

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

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

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

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

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

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Quiz summary

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1. Question

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Correct!

2. Question

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Well Done!

3. Question

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4. Question

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Excellent!

Speed-Distance-Time Formula

Quizzes

$(250)/(2000)$	$=$	$1/x$

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

$(250)/x$	$=$	$1/(480)$

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

$(680)/x$	$=$	$(60)/(30)$

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