Question

Walking at three-fourth of his usual speed, a man covers a certain distance in 2 hours more than the time he takes to cover the distance at his usual speed. What is the time taken by him to cover the same distance with his usual speed?
(A) 4 hours
(B) 9 hours
(C) 2 hours
(D) 6 hours

Answer 1

Hint:Let the usual speed of the man be x, the time taken by him be t and the distance traveled by him be d. The new speed of the man is three fourth of his usual speed that is $\dfrac{3}{4}x$ , the distance remains the same that is d and the time taken by the man is increased by 2 hours that is the new time is t+2. Using these values in the formula of speed one by one, we can find the correct answer.

Complete step by step answer:
We know that, $speed = \dfrac{{distance}}{{time}}$ .

The initial speed of the object can be written as, $x = \dfrac{d}{t}....(1)$

The new speed of the man can be written as, $\dfrac{3}{4}x = \dfrac{d}{{t + 2}}....(2)$

Using the value of x from (1) in (2), we get –
$
\dfrac{3}{4}(\dfrac{d}{t}) = \dfrac{d}{{t + 2}} \\
\Rightarrow \dfrac{3}{{4t}} = \dfrac{1}{{t + 2}} \\
\Rightarrow 3(t + 2) = 4t \\
\Rightarrow 3t + 6 = 4t \\
\Rightarrow t = 6 \\
$

Thus, the time taken by the man to cover the distance at the usual speed is 6 hours.

Note: The speed of an object is the rate at which it changes its position or we can say that it is the distance covered by the object per unit of time. So, when the distance covered by the object remains constant, the time taken by the object to cover the distance is inversely proportional to the speed of the object. In the given question, the speed of the man decreases, that's the time taken by him has increased.