Rates 4
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Question 1 of 4
1. Question
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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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
2. Question
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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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
3. Question
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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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
4. Question
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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Incorrect
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)`