Speed Problems: Conversion of Speed and Time Units

The red kangaroo hops across 120 meters in five seconds. What is the speed of the kangaroo in kilometers per minute?

Incorrect. [[snippet]]

Incorrect. [[snippet]]

Incorrect. You must have missed a decimal somewhere . . . [[snippet]]

Correct. First of all, assign each of the values in the question to the appropriate cell in the speed table. Then, convert the units using the replace with an equivalent principle. Replace the word meters with the equivalent $$\times \frac{1}{1{,}000}$$ kilometers. Go on to replace the word seconds with the equivalent $$\times \frac{1}{60}$$ minutes.

speed	time	distance
?	$$5$$ seconds	$$120$$ meters
?	$$5\times\frac{1}{60}$$ minutes	$$120\times \frac{1}{1{,}000}$$ kilometers

Simplifying the time and distance gives $$\frac{5}{60} = \frac{1}{12}$$ minutes and $$\frac{120}{1{,}000} = \frac{3}{25}$$ kilometers. Finally, calculate the speed. >$$\displaystyle \text{Speed} = \frac{\text{Distance}}{\text{Time}}$$ >>$$\displaystyle = \frac{\frac{3}{25} \mbox{ kilometers}}{\frac{1}{12} \mbox{minutes}}$$ >>$$\displaystyle = \frac{3}{25} \times \frac{12}{1} \mbox{ kilometers per minute}$$ >>$$\displaystyle = \frac{36}{25} \mbox{ kilometers per minute}$$ >>$$\displaystyle = 1.44 \mbox{ kilometers per minute}$$

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1.25

1.44

4

12.5

14.4