Question

A car travels a distance of 75 km at the speed of 25km/ hr. It covers the next 25 km of its journey at the speed of 5 km/hr and the last 50 km of its journey at the speed of 25 km/ hr. What is the average speed of the car?
A) 15 km/h
B) 12.5 km/h
C) 40 km/h
D) 25 km/h

Answer 1

Hint: The given journey can be divided into 3 parts and their respective times can be calculated as the speed and the distance are given. The average speed is calculated by dividing total distance by total time.
Formulas to be used:
 $ speed(S) = \dfrac{{dis\tan ce(D)}}{{time(T)}} $
\[Average{\text{ }}speed{\text{ }} = {\text{ }}\dfrac{{Total{\text{ }}distance}}{{Total{\text{ }}time}}\]

Complete step-by-step answer:
The journey of the car is divided into 3 parts, the respective times and speeds for each part is given as:
 $\Rightarrow speed(S) = \dfrac{{dis\tan ce(D)}}{{time(T)}} $ or
 $\Rightarrow T = \dfrac{D}{S} $ ________ (1)
Part 1:
Distance $ \left( {{D_1}} \right) $ = 75 km
Speed $ \left( {{S_1}} \right) $ = 25 km/h
Time = $ {T_1} $
Substituting these values in (1), we get:
 $\Rightarrow {T_1} = \left( {\dfrac{{75}}{{25}}} \right)hrs $
 $\Rightarrow {T_1} $ = 3 hours
Thus time taken to cover the first part of journey is 3 hours
Part 2:
Distance $ \left( {{D_2}} \right) $ = 25 km
Speed $ \left( {{S_2}} \right) $ = 5 km/h
Time = $ {T_2} $
Substituting these values in (1), we get:
 $\Rightarrow {T_2} = \left( {\dfrac{{25}}{5}} \right)hrs $
 $\Rightarrow {T_2} $ = 5 hours
Thus time taken to cover the second part of journey is 5 hours
Part 3:
Distance $ \left( {{D_3}} \right) $ = 50 km
Speed $ \left( {{S_3}} \right) $ = 25 km/h
Time = $ {T_3} $
Substituting these values in (1), we get:
 $\Rightarrow {T_3} = \left( {\dfrac{{50}}{{25}}} \right)hrs $
 $\Rightarrow {T_3} $ = 2 hours
Thus time taken to cover the third part of journey is 2 hours
Now,
\[\Rightarrow Average{\text{ }}speed{\text{ }} = {\text{ }}\dfrac{{Total{\text{ }}distance}}{{Total{\text{ }}time}}\] _______ (2)
Total distance (D):
D = $ {D_1} + {D_2} + {D_3} $
Substituting respective values, we get:
D = (75 + 25 + 50) km
D = 150 km
Total distance (D):
T = $ {T_1} + {T_2} + {T_3} $
Substituting respective values, we get:
T = (3 + 5 + 2) hours
T = 10 hours
Substituting the values of total distance and time in (2):
\[\Rightarrow Average{\text{ }}speed = \left( {\dfrac{{150}}{{10}}} \right)km/h\]
Average speed = 15 km/h
Therefore, the average speed of the car for the given journey is 15 km/h

Note: For the same distance, if there are two time intervals, the average speed is:
 $ {S_{av}} = \dfrac{d}{{{t_2} - {t_1}}} $ where,
 $ {S_{av}} $ = Average speed
d = Distance covered
 $ {t_2} $ and $ {t_1} $ = different time intervals
Average speed is a scalar quantity i.e. have only magnitude and no direction