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A boy reaches school in $30 minutes$ which is $4 km$ from his home. While coming back from school, he reaches home in $20 minutes$ . What is the average speed of the boy during the entire journey?

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10 km / h

9.6 km / h

8.5 km / h

5 km / h

answer is B.

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Detailed Solution

The average speed of the boy in the entire journey is

9.6 km / h

.
Given:
The distance between home and school

d = 4 km

,
Time taken while going

t_{1} = 30 \min

and
time taken in coming back

t_{2} = 20 \min

.
It is known that the average speed is defined as the total distance travelled by the total time taken during the process. Mathematically, it can be written as

Average Speed = \frac{Total distance}{Total time}

Now, according to the given values, the total time

(t)

is given as

t = t_{1} + t_{2}

On substituting the given values, we get

\Rightarrow t = 30 + 20

\Rightarrow t = 50 \min

Therefore, total time taken is

50 \min

\frac{5}{6} hour

.
Now, the total distance travelled

(D)

is given as

D = d + d

On substituting the given values, we get the total distance as

\Rightarrow D = 4 + 4

\Rightarrow D = 8 km

Therefore, the total distance is

8 km

.
Now, on substituting the values in the formula of the average speed, we get the average speed as

\Rightarrow Average Speed = \frac{Total distance}{Total time}

\Rightarrow Average Speed = \frac{8}{\frac{5}{6}}

\Rightarrow Average Speed = 9.6 km / h

Hence, the average speed of the boy is

9.6 km / h

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