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A man walks to a viewpoint and returns to the starting point by his car maintaining constant speed and thus takes a total time of 3 hours 15 minutes. He would have gained 3 hours by driving both ways. How long would it have taken for him to walk both ways with same walking speed?
6 hours 15 minutes
5 hours 15 minutes
6 hours 45 minutes
7 hours 30 minutes
6 hours 15 minutes
Let W be walking time and D be driving time. We know W+D = 3h 15m and 2D = (W+D) - 3h. Substitute D in the first equation to find W.
Let W be walking time and D be driving time. We know W+D = 3h 15m and 2D = (W+D) - 3h. Substitute D in the first equation to find W.
Establish Variables
Let W be the time taken to walk one way and D be the time taken to drive one way. Given W + D = 3 hours 15 minutes (195 minutes).
Use Gain Condition
Driving both ways saves 3 hours compared to walking to the viewpoint and driving back (which equals the time for walking one way). So, W + D - 2D = 3 hours. Thus, W - D = 3 hours (180 minutes).
Solve for W
Adding the equations: (W + D) + (W - D) = 195 + 180. 2W = 375 minutes. Therefore, W = 187.5 minutes.
Calculate Walk Both Ways
Time for walking both ways is 2W = 375 minutes, which is 6 hours and 15 minutes.
B: 5 hours 15 minutes is incorrect as it does not satisfy the drive time differential; C: 6 hours 45 minutes exceeds the calculated value; D: 7 hours 30 minutes is mathematically inconsistent with the given time gain.
A is correct because the total walk time is calculated as 375 minutes, which converts exactly to 6 hours 15 minutes.
In questions involving 'gaining time' by changing transport, always define the equation as: (Original Time) - (New Time) = (Time Saved). This prevents confusion between driving both ways and walking both ways.
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