Question

Without any stoppage a person travels a certain distance at an average speed of $42\,kmh{r^{ - 1}} $, and with stoppage he cover the same distance at an average speed of $28\,kmh{r^{ - 1}} $. How many minutes per hour does he stop?
(A) $14\,\min $
(B) $15\,\min $
(C) $28\,\min $
(D) $20\,\min $

Answer 1

Hint The time in minutes can be determined by finding the difference in the distance when the person travelled in one hour. Then by using the distance value in the time formula, the time in hours is determined, then the time in hours is converted to the minutes.
Useful formula
The time taken by the person is given by,
 $t = \dfrac{d}{v} $
Where, $v $ is the velocity or the speed where the person moves, $d $ is the distance where the person moves and $t $ is the time taken by the person to cover the distance.

Complete step by step answer
Given that,
Without any stoppage a person travels a certain distance at an average speed of, $v = 42\,kmh{r^{ - 1}} $.
With stoppage a person travels a certain distance at an average speed of $v = 28\,kmh{r^{ - 1}} $.
For one hour the distance covered is,
Without any stoppage a person travels a certain distance of, $d = 42\,km $.
With stoppage a person travels a certain distance of, $d = 28\,km $.
The difference in the distance travelled by the person is,
 $d = 42 - 28 $
By subtracting the terms in the above equation, then the above equation is written as,
 $d = 14\,km $
Now,
The time taken by the person is given by,
 $t = \dfrac{d}{v} $
By substituting the distance and the velocity or the speed in the above equation, then the above equation is written as,
 $t = \dfrac{{14}}{{42}} $
By dividing the terms in the above equation, then the above equation is written as,
 $t = 0.333\,hr $
To convert the time in hour to the minute, then the time is multiplied by the term $60 $, then the above equation is written as,
 $t = 0.333 \times 60\,\min $
By multiplying the terms in the above equation, then the above equation is written as,
 $t = 20\,\min $

Hence, the option (D) is the correct answer.

Note The time formula is derived from the velocity formula, as the velocity is equal to the distance divided by the time. From the equation, the time formula is derived. The time is directly proportional to the distance and inversely proportional to the speed.