Question

I travel the first part of my Journey at \[40{\text{kmph}}\] and the second part at \[60{\text{kmph}}\] and cover the total distance of \[240{\text{km}}\] to my destination in \[5\] hours. How long did the first part of my journey last?
A.4 hours
B.2 hours
C.3 hours
D.2 hours 24 minutes

Answer 1

Hint: Here, we will find the time taken to travel the first part of my Journey. We will assume the time taken in the first part and the second part of my Journey as some variables and by using the distance formula with the given speed and the assumed time, we will find the distance travelled. Then we will get the linear equation in one variable and solve the linear equation to find the time taken in the first part of my Journey. Thus the required time.

Formula Used:
 Distance is given by the formula ${\text{Distance}} = {\text{Speed}} \times {\text{Time}}$.

Complete step-by-step answer:
It is given that
Total distance covered by me $ = 240{\text{km}}$
Total time taken to cover the total distance $ = 5$ hours
Speed of the first part of my Journey $ = 40{\text{kmph}}$
Speed of the second part of my Journey $ = 60{\text{kmph}}$
Let ${x_1}$ be the time taken to travel the first part of my Journey and ${x_2}$ be the time taken to travel the second part of my Journey.
Let ${d_1}$ be the distance travelled in the first part of my Journey and ${d_2}$ be the distance travelled in the second part of my Journey
Since the total time taken to cover the distance is 5 hours, the time taken in the first part of my Journey should be added to the time taken in the second part of my Journey.
${x_1} + {x_2} = 5$
By substituting ${x_1} = x$ in the above equation, we get
$ \Rightarrow x + {x_2} = 5 \\
   \Rightarrow {x_2} = 5 - x \\ $
Distance travelled in the first part of my Journey with speed $40{\text{ }}kmph$ in \[x{\text{ }}hours\] is given by the distance formula
Distance travelled in the first part of my Journey, ${d_1} = x\left( {40} \right){\text{km}}$
Distance travelled in the second part of my Journey with speed $60{\text{ }}kmph$ in \[5 - x\] hours is given by the distance formula
Distance travelled in the second part of my Journey, ${d_2} = \left( {5 - x} \right)\left( {60} \right){\text{km}}$
Since the total distance covered is 240 km, the distance travelled in the first part of my Journey should be added to the distance travelled in the second part of my Journey.
${d_1} + {d_2} = 240$
By substituting the distance travelled in the first part and the second part of my Journey, we get
$ \Rightarrow 40x + \left( {5 - x} \right)60 = 240$
By multiplying the terms, we get
$ \Rightarrow 40x + 300 - 60x = 240$
By adding the like terms, we get
$ \Rightarrow 300 - 20x = 240$
By rewriting the equation, we get
$ \Rightarrow 20x = 300 - 240$
$ \Rightarrow 20x = 60$
Dividing by $20$ on both the sides, we get
$ \Rightarrow x = \dfrac{{60}}{{20}}$
$ \Rightarrow x = 3$ hours
Therefore, the time taken in the first part of my Journey is 3 hours.
Thus Option (C) is the correct answer.

Note: We know that the speed is defined as the ratio of the distance travelled by an object to the time taken by an object. Thus, we will find the distance formula by rewriting the speed formula. We should remember that we can convert ${\text{km/hr}}$ to ${\text{m/s}}$ by multiplying $\dfrac{5}{{18}}$ and also we can convert ${\text{m/s}}$ to ${\text{km/hr}}$by multiplying $\dfrac{{18}}{5}$. We should check whether all the units are in the same dimensions otherwise we will get wrong answers.