Quiz: Average Speed Problems
This quiz follows Lesson 3: Average Speed: Concepts and Formulas from the course Time, Speed & Distance: Core Concepts for Competitive Exams.
In this lesson you learned to:
- Define average speed and distinguish it from instantaneous speed.
- Apply the core formula: ##\text{Average Speed} = \dfrac{\text{Total Distance}}{\text{Total Time}}##.
- Handle journeys with equal distances using the harmonic mean shortcut ##\dfrac{2ab}{a+b}##.
- Handle journeys with unequal distances by summing distances and times separately.
- Avoid the classic mistake of averaging speeds arithmetically.
Work carefully with units, and remember: average speed is never simply the arithmetic mean of the speeds unless the times are equal. Good luck!
Q1. Average speed is best defined as:
Average speed is the total distance covered divided by the total time taken for the whole journey, not an instantaneous value.
Q2. A car covers ##240## km in ##4## hours. What is its average speed?
Average speed ##= \dfrac{240}{4} = 60## km/h.
Q3. A cyclist travels ##30## km at ##15## km/h and then ##30## km at ##10## km/h. What is the average speed for the whole journey?
Equal distances: average speed ##= \dfrac{2ab}{a+b} = \dfrac{2 \times 15 \times 10}{15+10} = \dfrac{300}{25} = 12## km/h.
Q4. A train covers the first half of a journey at ##40## km/h and the second half at ##60## km/h. Its average speed is:
Equal distances: ##\dfrac{2 \times 40 \times 60}{40+60} = \dfrac{4800}{100} = 48## km/h.
Q5. A student averages ##60## km/h and ##40## km/h over two equal distances. A common mistake is to answer:
The arithmetic mean ##\dfrac{60+40}{2} = 50## km/h is the classic error; the correct average speed is ##48## km/h.
Q6. A man travels ##100## km at ##50## km/h and then ##150## km at ##75## km/h. His average speed is:
Total distance ##= 250## km; total time ##= 2 + 2 = 4## h; average speed ##= \dfrac{250}{4} = 62.5## km/h.
Q7. Which formula correctly gives average speed for a multi-segment journey?
Average speed is total distance divided by total time, i.e. ##\dfrac{d_1+d_2}{t_1+t_2}##.
Q8. A car travels ##120## km at ##60## km/h and returns the same distance at ##40## km/h. Its average speed for the round trip is:
Equal distances: ##\dfrac{2 \times 60 \times 40}{60+40} = \dfrac{4800}{100} = 48## km/h.
Q9. If a body covers equal distances at speeds ##a## and ##b##, its average speed is:
For equal distances the average speed is the harmonic mean ##\dfrac{2ab}{a+b}##.
Q10. A runner covers ##5## km in ##25## minutes and ##10## km in ##50## minutes. His average speed is:
Total distance ##= 15## km; total time ##= 75## min ##= 1.25## h; average speed ##= \dfrac{15}{1.25} = 12## km/h.
Q11. Average speed differs from instantaneous speed because average speed:
Average speed uses total distance and total time over the whole journey, whereas instantaneous speed refers to a single moment.
Q12. A bus covers ##90## km at ##45## km/h and ##60## km at ##30## km/h. Its average speed is:
Total distance ##= 150## km; total time ##= 2 + 2 = 4## h; average speed ##= \dfrac{150}{4} = 37.5## km/h.
Q13. Two equal distances are covered at ##20## km/h and ##30## km/h. The average speed is:
##\dfrac{2 \times 20 \times 30}{20+30} = \dfrac{1200}{50} = 24## km/h.
Q14. A common mistake in average speed problems is to:
Simply averaging the speeds arithmetically is wrong unless the times for each segment are equal.
Q15. A car covers ##150## km in ##3## hours and then ##100## km in ##2## hours. Its average speed is:
Total distance ##= 250## km; total time ##= 5## h; average speed ##= \dfrac{250}{5} = 50## km/h.
Q16. A person walks the first ##2## km at ##4## km/h and the next ##2## km at ##6## km/h. The average speed is:
Equal distances: ##\dfrac{2 \times 4 \times 6}{4+6} = \dfrac{48}{10} = 4.8## km/h.
Q17. If total distance is ##D## and total time is ##T##, average speed equals:
Average speed is total distance divided by total time, ##\dfrac{D}{T}##.
Q18. A truck travels ##60## km at ##30## km/h and ##40## km at ##20## km/h. Its average speed is:
Total distance ##= 100## km; total time ##= 2 + 2 = 4## h; average speed ##= \dfrac{100}{4} = 25## km/h.
Q19. For equal distances at speeds ##a## and ##b##, the average speed is always:
The harmonic mean ##\dfrac{2ab}{a+b}## is always less than or equal to the arithmetic mean ##\dfrac{a+b}{2}## (equal only when ##a=b##).
Q20. A cyclist covers ##12## km at ##12## km/h and ##18## km at ##9## km/h. The average speed is:
Total distance ##= 30## km; total time ##= 1 + 2 = 3## h; average speed ##= \dfrac{30}{3} = 10## km/h.