A boy goes from his house to school by bus at a speed of $20\ km\ h^{-1}$ and returns back through the same route at a speed of $30 \ km\ h^{-1}$. The average speed of his journey is ______.
✓
$24 \ km\ h ^{-1}$
B
$25\ km \ h ^{-1}$
C
$30 \ km \ h ^{-1}$
D
$20 \ km \ h ^{-1}$
Answer
Correct option: A.
$24 \ km\ h ^{-1}$
A boy goes from his house to school by bus at a speed of $20 \ km \ h ^{-1}$ and returns back through the same route at a speed of $30 \ km \ h ^{-1}$. The average speed of his journey is $\underline{ 2 4\ km\ h ^{-1}}$.
Explanation:
Let the distance between the school and the house is $km$.
speed of the boy from house to school $=20 \ km / hr$.
Using formula, Time taken $=\frac{distance}{speed}$
So, time taken $=\frac{x}{20}$ hours.
Also, Speed of the boy from school to the house $=30 \ km / hr$
So, time taken $=\frac{x}{30}$ hours.
Total time taken $=\frac{x}{20}+\frac{x}{30}=\frac{x}{12}$ hours
Also total distance covered by boy $=x+x=2 x \ km$.
Using formula,
Average speed $=\frac{Total\ distance}{Total\ time}$
$=\frac{2 x}{\frac{x}{12}}$
$=2 \not x ^{\prime} \times \frac{12}{\not x}$
$=24 \ km / hr $
Thus, average speed of the boy's journey is $24 \ km\ h ^{-1}$.
A boy goes from his house to school by bus at a speed of $20 \ km\ h^{-1}$ and returns back through the same route at a speed of $30\ \ km\ h^{-1}$. The average speed of his journey is $........$
✓
$24\ km\ h ^{-1}$
B
$25 \ km \ h ^{-1}$
C
$30\ km\ h ^{-1}$
D
$20\ km \ h ^{-1}$
Answer
Correct option: A.
$24\ km\ h ^{-1}$
A boy goes from his house to school by bus at a speed of $20\ km \ h ^{-1}$ and returns back through the same route at a speed of $30\ km\ h ^{-1}$. The average speed of his journey is $\underline{ 2 4\ km\ h ^{-1}}$.
Explanation :
Let the distance between the school and the house is $km$.
speed of the boy from house to school $=20\ km / hr$.
Using formula, Time taken $=\frac{distance}{speed}$
So, time taken $=\frac{x}{20}$ hours.
Also, Speed of the boy from school to the house $=30\ km / hr$
So, time taken $=\frac{x}{30}$ hours.
Total time taken $=\frac{x}{20}+\frac{x}{30}=\frac{x}{12}$ hours
Also total distance covered by boy $=x+x=2 x\ km$.
Using formula,
Average speed $=\frac{Total\ distance}{Total\ time}$
$=\frac{2 x}{\frac{x}{12}}$
$=2 \not x ^{\prime} \times \frac{12}{\not x}$
$=24\ km / hr$
Thus, average speed of the boy's journey is $24\ km \ h ^{-1}$.