Question

A car travels first 100 km in $ 2\dfrac{1}{2} $ hours and the next 30 km in $ \dfrac{1}{2} $ hour. What is its average speed?
A) $ \dfrac{{130}}{2} $ km/h
B) $ \dfrac{{130}}{3} $ km/h
C) $ \dfrac{{100}}{3} $ km/h
D) None of these

Answer 1

Hint: The distance and time for respective parts of the travel are given which can be used to find the total speed and total time. These values are then substituted in the formula for average speed:
 $ {V_{av}} = \dfrac{D}{T} $ where,
 $ {V_{av}} $ = Average speed
D = Total distance covered
T = Total time taken

Complete step-by-step answer:
The distance covered in the first part of the travel $ \left( {{D_1}} \right) $ = 100 km
The distance covered in the second part of the travel $ \left( {{D_2}} \right) $ = 30 km
Total distance (D) covered is the sum of the two distance covered:
$\Rightarrow$ D = $ {D_1} $ + $ {D_2} $
Substituting the values:
D = (100 + 30) km
D = 130 km ________ (1)
And
The time taken to travel in the first part $ \left( {{T_1}} \right) $ = $ 2\dfrac{1}{2} $ hours
The time taken to travel in the second part $ \left( {{T_2}} \right) $ = $ \dfrac{1}{2} $ hour
Total time taken is the sum of the two times taken for respective parts of travel:
$\Rightarrow$ T = $ {T_1} $ + $ {T_2} $
Substituting the values:
 $
 \Rightarrow T = \left( {2\dfrac{1}{2} + \dfrac{1}{2}} \right)hrs \\
\Rightarrow T = \left( {\dfrac{5}{2} + \dfrac{1}{2}} \right)hrs \\
\Rightarrow T = \left( {\dfrac{6}{2}} \right)hrs \\
  $ [in improper fraction]
T = 3 hrs ____________ (2)
Now,
The average speed is given by dividing the total distance covered by total time taken:
 $\Rightarrow {V_{av}} = \dfrac{D}{T} $
Substituting the values from (1) and (2) , we get:
 $\Rightarrow {V_{av}} = \left( {\dfrac{{130}}{3}} \right)km/h $
Therefore, the average speed of the car for the given travel will be $ \dfrac{{130}}{3}km/h $ and thus the correct option is B).

So, the correct answer is “Option B”.

Note: $ 2\dfrac{1}{2} $ is a mixed fraction whereas $ \dfrac{1}{2} $ is a proper fraction, we cannot perform any mathematical operation on them, so we convert the mixed fraction to improper fraction:
 $
\Rightarrow 2\dfrac{1}{2} = \dfrac{{2 \times 2 + 1}}{2} \\
\Rightarrow 2\dfrac{1}{2} = \dfrac{5}{2} \\
  $
And then perform the mathematical operations.