Question

A car travels first 30 km with a uniform speed of $60km{h^{ - 1}}$and then next 30 km with a uniform speed of $40km{h^{ - 1}}$. Calculate the total time of journey.
A) $50 min$
B) $75 min$
C) $60 min$
D) $100 min$

Answer 1

Hint: Here we know the basic formula for speed, distance and time. Apply the speed-distance-time formula for the first 30km and then for the next 30km and calculate the time taken for each case and for the total time taken add the two times together.

Complete step by step answer:
Find the total time taken:
$S = \dfrac{D}{T}$ .
Here:
S = Speed.
D = Distance.
T = Time Taken.
For the first 30km.
${T_1} = \dfrac{{{D_1}}}{{{S_1}}}$.
$ \Rightarrow {T_1} = \dfrac{{30}}{{60}}$.
Time required to cover first 30 km is:
$ \Rightarrow {T_1} = \dfrac{1}{2}hr = 30\min $.
Similarly, Time required to complete the next 30km.
${T_2} = \dfrac{{{D_2}}}{{{S_2}}}$.
Put in the given value in the above equation and solve,
$ \Rightarrow {T_2} = \dfrac{{30}}{{40}}$.
Time required to cover the next 30 km is:
$ \Rightarrow {T_2} = \dfrac{3}{4}hr = 45\min $.
Total time taken to cover 60km is:
$T = {T_1} + {T_2}$.
Add the two times that we have found out:
 $ \Rightarrow T = 45 + 30$.
The time taken is:
$ \Rightarrow T = 75\min $.

Option B is correct. A car travels first 30 km with a uniform speed of $60km{h^{ - 1}}$and then next 30 km with a uniform speed of $40km{h^{ - 1}}$. The total time journey it takes is 75 min.

Note: We know that in order to get time we have to divide the distance with speed. Before applying the relation check the formula is dimensionally correct. $T = \dfrac{D}{S} \Rightarrow hour = \dfrac{{km}}{{km/hour}} \Rightarrow hr = hr$. Here the dimension in the R.H.S is equal to the L.H.S. And hence the formula is correct.