Rates 4

Question 1 of 4

A dog is running at

$30 \text(km/hour)$ . How long will the dog take to travel

$120 \text(km)$ ?

(4) $\text(hours)$

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Mute

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 time.

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

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

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

Next, substitute the known values to the derived formula.

$\text(Speed)$	$=$	$30 \text(km/hour)$
$\text(Distance)$	$=$	$120 \text(km)$

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

	$=$	$\frac{\color{#9a00c7}{120\;\text{km}}}{\color{#00880a}{30\;\text{km/hour}}}$	Substitute known values

	$=$	$4 \text(hours)$	km cancels out

$\text(Time)=4 \text(hours)$

Question 2 of 4

A jet flies at a speed of

$680 \text(km/hour)$ . Use the speed-distance-time formula to determine how far it can travel in

$30$ minutes.

(340) $\text(km)$

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Mute

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.

$\text(Speed)$	$=$	$(680 \text(km))/(\text(hour))$

$\text(Time)$	$=$	$1/2 \text(hour)$

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

	$=$	$\color{#00880a}{\frac{680\;\text{km}}{\text{hour}}}\cdot\color{#e65021}{\frac{1}{2}\text{hours}}$	Substitute known values

	$=$	$340 \text(km)$	Hours cancel out

$\text(Distance)=340 \text(km)$

Question 3 of 4

A train travelled

$360\text(km)$ in

$1$ hour and

$20$ minutes. What is the speed of the train?

(270) $\text(km/hour)$

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Mute

Speed-Distance-Time Formula

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

First, convert the minutes into hours.

$1 \text(hour)$

$=$

$60 \text(minutes)$

$20xx1/(60)$	$=$	$20/60$

	$=$	$1/3$	Simplify

The total time is

$1 1/3 \text(hours)$ .

Next, substitute the known values to the formula.

$\text(Distance)$	$=$	$360 \text(km)$

$\text(Time)$	$=$	$1 1/3 \text(hour)$

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

	$=$	$\frac{\color{#9a00c7}{360\;\text{km}}}{\color{#e65021}{1\frac{1}{3}\;\text{hours}}}$	Substitute known values

	$=$	$270 \text(km/hour)$	Evaluate

$\text(Speed)=270 \text(km/hour)$

Question 4 of 4

A car is travelling at

$80 \text(km/hour)$ . How long will it take to travel

$500 \text(km)$ ?

Round your answer in decimal form

(6.25) $\text(hours)$

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Mute

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 time.

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

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

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

Next, substitute the known values to the derived formula.

$\text(Speed)$	$=$	$80 \text(km/hour)$
$\text(Distance)$	$=$	$500 \text(km)$

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

	$=$	$\frac{\color{#9a00c7}{500\;\text{km}}}{\color{#00880a}{80\;\text{km/hour}}}$	Substitute known values

	$=$	$6.25 \text(hours)$	km cancels out

$\text(Time)=6.25 \text(hours)$

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Quiz summary

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1. Question

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Keep Going!

Speed-Distance-Time Formula

2. Question

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Exceptional!

Speed-Distance-Time Formula

3. Question

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Well Done!

Speed-Distance-Time Formula

4. Question

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Great Work!

Speed-Distance-Time Formula

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