Question

A car travelling at a speed of $40 \text{Km}/\text{hour}$ can complete a journey in 9 hours. How long will it take to travel the same distance at $60 \text{Km}/\text{hour}$ ?
$
  {\text{A}}{\text{. 6 hours}} \\
  {\text{B}}{\text{. 3 hours}} \\
  {\text{C}}{\text{. 4 hours}} \\
  {\text{D}}{\text{. 4}}\dfrac{1}{4}{\text{ hours}} \\
$

Answer 1

Hint: To find the time taken, we apply the formula of speed using both the given speeds, as the distance travelled is equal, we can equate them. In solving the relation we obtain the time taken.

Complete Step-by-Step solution:
Given Data,
A speed of $40 \text{Km}/\text{hour}$ covers a distance in 9 hours.
Let the distance travelled be a variable x.
We know the speed of a car which travelled a distance d in time t is given by s =$\dfrac{{\text{d}}}{{\text{t}}}$.
Now at 40$\text{Km}/\text{hour}$, we get
40 = $\dfrac{{\text{d}}}{{540}}$ (1 hour = 60 min, hence 9 hours = 9 × 60 = 540 min)
⟹d = 40 × 540 units.

Given the distance travelled at 60$\text{Km}/\text{hour}$ is also same, hence the speed equation is
60 = $\dfrac{{40{\text{ }} \times {\text{ 540}}}}{{\text{T}}}$
$ \Rightarrow {\text{T = }}\dfrac{{40 \times 540}}{{60}} = 360{\text{ min}}$
I.e. $\dfrac{{360}}{{60}} = 6$hours.
Hence the same distance travelled by the car at 60$\text{Km}/\text{hour}$ takes 6 hours.
Hence Option A is the correct answer.

Note: In order to solve questions of this type the key is to know the formula of speed. We must observe the question says the distance travelled at both speeds is the same, this is an important step in solving this problem. The relation between an hour and minutes is that 1 hour = 60 minutes and 3600 seconds.