Question

A man can reach a certain place in $30$ hours. If he reduces his speed by $\dfrac{1}{{15}}$th, he goes $10km$ less in that time. Find his speed in $\dfrac{km}{hr}$

Answer 1

Hint: First we have to define what the terms we need to solve the problem are.
Since we need to find the speed of the given problem, which is a man can reach the desired place in thirty hours, and if the man reduces the speed one by fifteen.
At that speed the man reaches ten kilometers less than the time before, and we need to find the speed of that man by using the speed, distance and time formula.

Formula used: $speed = \dfrac{{dis\tan ce}}{{time}}$where distance is the total area covered by the man and time taken is the time.

Complete step by step answer:
Let us fix the unknown man as X so that we can apply this in the formulas and find the speed.
So, let X be that man, we need to find the speed of X concerning kilometers per hour.
Since the distance covered in $30$ hours can be reframed with X.
Thus, we get $30X$(kilometer per hour); Since we need to find the new speed using the help of the two given things speed and distance.
Thus, new speed is $X - \dfrac{X}{{15}}$ the equation that can be rewritten as $\dfrac{{14X}}{{15}}$(kilometer per hour).
Hence the distance covered at $30$hours with the new speed is $\dfrac{{14X}}{{15}} \times 30 \Rightarrow 28X$ a new speed and now the X goes $10km$ less in that time.
Thus, we get $30X - 28X = 10km$ (overall speed minus the new speed).
Further solving we get $X = 5km$.
Hence the man speed is$5\dfrac{km}{hr}$.

Note: since using the same formula $speed = \dfrac{{dis\tan ce}}{{time}}$; we can also able to find the distance and time; where distance is the person covered and time is the time taken to covered overall.
Also $\dfrac{km}{hr}$ means a person covered a kilometer at the time taken is the hour; time is taken to cover that distance.