Mohan walks a certain distance and rides back in 6 hours and 15 minutes. If he…

Step-by-Step Solution

To solve this, let's represent the time taken to walk a certain distance as w and the time taken to ride as r.

1. Translate the given conditions into equations:

   • Walking one way and riding back: w + r = 6 hours and 15 minutes

     • Convert 15 minutes to hours: 15/60 = 0.25 hours.

     • w + r = 6.25 or 25/4 hours. (Equation 1)

   • Walking both ways: w + w = 2w = 7 hours and 45 minutes

     • Convert 45 minutes to hours: 45/60 = 0.75 hours.

     • 2w = 7.75 or 31/4 hours. (Equation 2)

2. Solve for w and r:

   • From Equation 2: w = 31/8 hours.

   • Substitute w into Equation 1: 31/8 + r = 25/4

   • r = 25/4 - 31/8

   • r = 50/8 - 31/8 = 19/8 hours.

3. Calculate the time for riding both ways (2r):

   • 2r = 2 * (19/8) = 19/4 hours.