Speed problems: The Speed Table - Handling Speed Problems with Data Overload

Tom drives to take a GMAT test at an average speed of 50 kilometers per hour. The moment he arrives at the test location, he realizes that he made a mistake and the test is actually the next day. He immediately returns home the same way, this time at an average speed of 30 kilometers per hour. If Tom drives 40 kilometers from his home to the GMAT test location, what is Tom's average speed, in kilometers per hour, during his entire journey?

Then calculate the time by dividing distance by speed. Add the times and distances up to find the total: | | SPEED (KM/H) | TIME (HOURS) | DISTANCE (KM) | |-----------|-------------------------|-------------------------------------------|-------------------------| | To test | $$50$$ | $$\color{blue}{\frac{40}{50} = \frac{4}{5}}$$ | $$40$$ | | Back home | $$30$$ | $$\color{blue}{\frac{40}{30} = \frac{4}{3}}$$ | $$40$$ | | Total | $$\color{red}{?}$$ | $$\color{blue}{\frac{4}{5}+\frac{4}{3}=\frac{32}{15}} ~~~~$$ | $$\color{blue}{40+40=80}$$ | Finally, use the average speed formula to calculate the answer: >$$\displaystyle \text{Average speed}= \frac{80\ \text{km}}{\frac{32}{15}\ \text{hour}}$$ >>>>$$\displaystyle = 80 \div \frac{32}{15}\ \text{kilometers per hour}$$ >>>>$$\displaystyle = 80 \times \frac{15}{32}\ \text{kilometers per hour}$$ >>>>$$\displaystyle = \frac{5 \times 15}{2}\ \text{kilometers per hour}$$ >>>>$$\displaystyle = 37.5\ \text{kilometers per hour}$$

Incorrect. You are looking for the average speed, which is the _total_ distance (way there $$+$$ way back) divided by the _total_ time (way there $$+$$ way back.) This answer is a trap: 40 km/h is the average of the two speeds, _not_ the average speed. Next time, eliminate this kind of answer choice right away.

Incorrect. [[snippet]]

Incorrect. [[snippet]]

Incorrect. [[snippet]]

Correct. You cannot miss the fact that this is an "average speed question," but before you can apply the average speed formula, you should organize the {color:dark-green}information in the question{/color} in a Speed table. | | SPEED (KM/H) | TIME (HOURS) | DISTANCE (KM) | |-----------|-------------------------|-------------------------------------------|-------------------------| | To test | {color:dark-green}$$50$${/color} | | {color:dark-green}$$40$${/color} | | Back home | {color:dark-green}$$30$${/color} | | {color:dark-green}$$40$${/color} |

35

37.5

40

42.5

45

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