question_answer

A car covers four successive three km. stretches at speeds of 10 kmph. 20 kmph, 30 kmph and 60 kmph respectively. What is its average speed over this distance?

A)  20 kmph                    

B)  25 kmph

C)  30 kmph        

D)       40 kmph

Correct Answer: A

Solution :

 Starting   \[\therefore \]   Total distance \[=3\times 4\] \[=12\,km\] Total time \[=\frac{\text{Distance}}{Speed}\] \[=\left( \frac{3}{10}+\frac{3}{20}+\frac{3}{30}+\frac{3}{60} \right)\] hours \[=3\left( \frac{1}{10}+\frac{1}{20}+\frac{1}{30}+\frac{1}{60} \right)\] hours \[=3\left( \frac{6+3+2+1}{60} \right)\] \[=3\times \frac{12}{60}=\frac{3}{5}\] hours \[\therefore \]   Required speed             \[=\frac{Total\text{ }distance}{~Total\text{ }time}\] \[=\frac{12}{\frac{3}{5}}=\frac{12\times 5}{3}\] \[=20\text{ }kmph\]