Bunuel wrote:

Ron walks to a viewpoint and returns to the starting point by his car 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.

A. 8 h 45 min

B. 7 h 45 min

C. 6 h 45 min

D. 5 h 30 min

E. None of these

We let the walk rate = w and the car rate = c. We let the distance = d. We also convert 6 hours 45 minutes to 6 3/4 hours.

We can create the equations:

d/c + d/w = 6 3/4

and

d/c + d/c = 4 3/4

If we simply the second equation, we have:

2d/c = 19/4

d/c = 19/8

Substituting d/c = 19/8 in d/c + d/w = 6 3/4, we have:

19/8 + d/w = 6 3/4

d/w = 6 3/4 - 19/8 = 54/8 - 19/8 = 35/8

Notice that d/w is the one-way walking time, so the round-trip walking time would be:

2d/w = 2 x 35/8 = 35/4 = 8 3/4 hours = 8 hours 45 minutes

Answer: A

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