Question

A marathon runner completes a full marathon of 42 km in 4 hours and 30 minutes. What is his speed in m/sec (rounded to one decimal place)?

Answer 1

Hint: In order to solve this question, we should know the formula of speed which states that speed is calculated by finding the ratio of the distance travelled by an object to the time taken by the object. Mathematically, we can write it as,
${\text{Speed}} = \dfrac{{{\text{Distance travelled}}}}{{{\text{Time taken}}}}$

Complete step-by-step answer:
In this question, we are asked to find the speed attained by a marathon runner who completes a full marathon of 42 Km in 4 hours and 30 minutes and also the speed is needed to be calculated in m/sec.
So, let us consider the speed of the marathon runner is x Km/hr.
And we know that speed of an object is defined as the ratio of the distance travelled by an object to the time taken by the object to travel that distance.
Mathematically, we can write it as,
${\text{Speed}} = \dfrac{{{\text{Distance travelled}}}}{{{\text{Time taken}}}}$
We know Distance Travelled = 42 Km
Time taken = 4 hours and 30 minutes = 4.5 hours
To this equation, we will substitute the values of distance and time, we will get speed as the value of x,
$ \Rightarrow x = \dfrac{{42}}{{4.5}} = \dfrac{{28}}{3}\,km/hr$
A kilometre is being used officially for expressing large distances between two places which are far enough.
Definition of meters: A meter (m) is the base unit of length or International System of Units (SI).
Therefore, 1km = 1000 meters
Definition of Hour: A period of time which is equal to 60 minutes or 3600 seconds.
Definition of second: It is the smallest unit of time and also the SI unit.
$ \Rightarrow 1\;hr = 3600\;\sec $
Now, $\dfrac{{28}}{3}\,km/hr$need to be converted to meters per second.
Let y be $\dfrac{{28}}{3}\,km/hr$ which is needed to convert into meter per second
$ \Rightarrow y{\text{ = }}\dfrac{{28}}{3}\dfrac{{{\text{km}}}}{{hr}}$
$ \Rightarrow y = \dfrac{{28}}{3}\left( {\dfrac{{1000\;m}}{{3600\;\sec }}} \right)$
$ \Rightarrow y = \dfrac{7}{3}\left( {\dfrac{{10\;m}}{{9\;\sec }}} \right)$
$ \Rightarrow y = \dfrac{{70\;m}}{{27\;\sec }} = 2.59\;m/\sec $
As we need to round of the speed to one decimal place
$ \Rightarrow y = 2.6\;m/\sec $
Therefore, marathon runner speed is equal to 2.6 meters per second.


Note: In this question, the possible mistake one can make is by not covering the minutes into seconds or maybe by ignoring the measurements of Distance and time given in km and hr respectively. We should know the conversion rule of minutes to seconds, that is 1 minute = 60 seconds and hours to second, that is 1 hour = 60 minutes = 60 $ \times $ 60 seconds, and also 1 km = 1000 m.