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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 6 hours 45 minutes. He would have gained 2 hours by driving both ways. How long would it have taken for him to walk both ways with same walking speed?
8 hours 30 minutes
9 hours 15 minutes
7 hours 45 minutes
8 hours 45 minutes
8 hours 45 minutes
Let Walk = W, Car = C. Given W+C = 6h 45m and (C+C) = (W+C) - 2h. Calculate C, then solve for 2W = 2(W+C) - 2C.
Let Walk = W, Car = C. Given W+C = 6h 45m and (C+C) = (W+C) - 2h. Calculate C, then solve for 2W = 2(W+C) - 2C.
Convert total time to minutes
6 hours 45 minutes = (6 * 60) + 45 = 360 + 45 = 405 minutes. Let W be walking time and C be car time. So, W + C = 405.
Calculate driving time
Driving both ways saves 2 hours (120 minutes). So, C + C = 405 - 120 = 285 minutes.
Find walking time
Since W + C = 405, then 2 * (W + C) = 810. Substituting 2C = 285, we get 2W = 810 - 285 = 525 minutes.
Final conversion
525 minutes / 60 = 8 hours and 45 minutes.
A: Incorrect, 8h 30m is less than the calculated 8h 45m. B: Incorrect, 9h 15m is more than the required result. C: Incorrect, 7h 45m is too short for the walk.
D is correct because 2W = 2(W+C) - 2C = 810 - 285 = 525 minutes, which is 8 hours 45 minutes.
Always convert units to the smallest unit (minutes) first to avoid fractional confusion during calculation.
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