Question & Answer
QUESTION

A man takes 5hours 45 minutes in walking to a certain place and riding back. He would have gained 2hours by riding back both ways. The time he would take to walk both ways is

ANSWER Verified Verified
Hint: Calculate the time taken by the man to ride both ways by subtracting 2hours from the time taken by the man to walk one way and ride back. Divide this time to 2 to calculate the time taken by the man to ride one day. Calculate the time taken by the man to walk one way by subtracting the time taken by the man to walk one way from the time taken by the man to walk one way and ride back. Now multiply this time by 2 to calculate the time taken by the man to walk both ways.

Complete step by step answer:
We have data regarding the time taken by the man to walk and ride back over a certain distance. We have to calculate the time taken by him if he walks both ways.
We know that he takes 5hours 45minutes to walk a certain distance and ride back. We will convert 45minutes into hours.
We know that $1hr=60\min $. To convert ‘x’ minutes into hours, we will divide ‘x’ by 60.
Thus, we can write 45minutes into hours as $45\min =\dfrac{45}{60}hr=\dfrac{3}{4}hr$.
So, the total time taken by the man to walk one way and ride back the other is $5hr45\min =\left( 5+\dfrac{3}{4} \right)hr=\dfrac{20+3}{4}hr=\dfrac{23}{4}hr$.
We know that man took 2 hours less than $\dfrac{23}{4}hr$ to ride both ways.
Thus, the time taken by the man to ride both ways is $=\dfrac{23}{4}-2=\dfrac{23-8}{4}=\dfrac{15}{4}hr$.
To calculate the time taken by the man to ride one way, we will divide the time taken by the man to ride both ways by 2. Thus, time taken by the man to ride one way is $=\dfrac{\dfrac{15}{4}}{2}=\dfrac{15}{4}\times \dfrac{1}{2}=\dfrac{15}{8}hr$.
We will now calculate the time taken by the man to walk one way. To do so, we will subtract the time taken by the man to ride one way from the time taken by the man to walk one way and ride back.
Thus, the time taken by the man to walk one way is $=\dfrac{23}{4}-\dfrac{15}{8}=\dfrac{46-15}{8}=\dfrac{31}{8}hr$.
To calculate the time taken by the man to walk both ways, we will multiply the time taken by the man to walk both ways by 2. Thus, the time taken by the man to walk both ways is $=2\times \dfrac{31}{8}=\dfrac{31}{4}hr$.
We can convert this time into minutes and hours. Thus, we have $\dfrac{31}{4}hr=\left( 7+\dfrac{3}{4} \right)hr$.
To convert the fraction of hours into minutes, multiply it by 60. Thus, we have $\dfrac{31}{4}hr=\left( 7+\dfrac{3}{4} \right)hr=7hr+\dfrac{3}{4}\times 60\min =7hr45\min $.
Hence, the man takes 7hours 45minutes to walk both ways.

Note: One must keep in mind that the distance that the man covers remains constant. Also, the man walks or rides at the same speed all the time. We can also solve this question by assuming that the man covers x km each time.