Question

I walk a certain distance and ride back taking a total time of 37 minutes. I could walk both ways in 55 minutes. How long would it take to ride back both ways?

Answer 1

Hint: Calculate the time taken to cover the distance one way by dividing the time taken by the man to walk both ways by 2. Write an equation relating the time taken by the man to walk one way and ride on the way back. Solve this equation to find the time taken by the man to ride one way. Multiply this time by 2 to calculate the time taken by man to ride both ways.

Complete step-by-step answer:
We know that a man takes 37 minutes to walk a certain distance and then ride back. The same man takes 55 minutes to walk both ways. We have to calculate the time taken by the man to ride both ways.
As we know that the time taken by the man to walk both ways is 55 minutes, we will divide this time by 2 to calculate the amount of time taken by the man to walk one way.
Thus, the time taken by the man to walk one way is \[=\dfrac{55}{2}=27.5\] minutes.
We know that the time taken by the man to walk one way and ride back is 37 minutes and time taken by man to walk one way is 27.5 minutes. To calculate the time taken by the man to ride one way, we will subtract the time taken by man to walk one way from the total time taken by man to walk and ride.
Thus, the time taken by the man to ride one way is \[=37-27.5=9.5\] minutes.
To calculate the time taken by the man to ride both ways, we will multiply the time taken by the man to ride one way by 2.
Thus, the time taken by the man to ride both ways is \[=2\times 9.5=19\] minutes.
Hence, the man takes 19 minutes to ride back both ways.

Note: One must keep in mind that the distance remains constant during the journey and the man travels with the same speed during a particular way. This is a question involving basic unitary methods. Unitary method helps to find the value of a unit from the value of a multiple.