Question

Walking $\dfrac{6}{7}th$ of his usual speed, a man is $12\,minutes$ too late.What is the usual time taken by him to cover that distance?

Answer 1

Hint: In order to answer this question, to find out the usual time taken by the man, we will first assume the usual distance and speed in different variables and then we will also write the original time taken with the help of the assumed distance and speed. And then we will find the new speed and the new time as per the question. And finally, according to the question, we will write the equation that indicates the usual time taken by him. Then we will solve for it.

Complete step by step answer:
Given that- Walking $\dfrac{6}{7}th$ of his usual speed, a man is $12\,minutes$ too late. The usual time taken by him to cover that distance has to be found out. Let the distance covered and the original speed be $x\,and\,y$ respectively. Now, as we know the formula that relates time, distance and the speed:
$\text{Time} = \dfrac{\text{Distance}}{\text{Speed}}$
Thus, the original time taken by him is, $time = \dfrac{x}{y}$ .
Walking $\dfrac{6}{7}th$ of his usual speed, that means-
New speed is $\dfrac{6}{7}y$ and new time is,
$\text{New time} = \dfrac{\text{Distance}}{\text{New speed}} \\
\Rightarrow \text{New time} = \dfrac{x}{{\dfrac{6}{7}y}} \\
\Rightarrow \text{New time} = \dfrac{{7x}}{{6y}}$

So, the new time is $\dfrac{{7x}}{{6y}}$. Now, it is given that the man is $12\,minutes$ too late, i.e..
$\text{New time - Original time} = 12 \\
\Rightarrow \dfrac{{7x}}{{6y}} - \dfrac{x}{y} = 12 \\
\Rightarrow \dfrac{x}{y}(\dfrac{7}{6} - 1) = 12 \\
\Rightarrow \dfrac{x}{y}(\dfrac{1}{6}) = 12 \\
\therefore \dfrac{x}{y} = 72 \\ $
Hence, the usual time taken by him to cover that distance is $72\,minutes$ or $1\,hr\,12\,minutes$.

Note: A distance-time graph, which displays how the speed of an item varies as time passes, is a useful method to see how it changes. As long as the other two variables are known, the relationship between speed, distance, and time may be utilised to compute any of the three variables. For example, the distance travelled divided by the speed equals the travel time. Distance travelled can be calculated by multiplying speed and time together.