Question 1134632
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Here is yet another way to solve the problem.<br>
As tutor @ikleyn states in her response, it is always worthwhile to know different ways to solve problems.  In a particular problem, one method might be far easier to use than another.<br>
The distances both ways are the same, and the ratio of the rates is 3:5.  That means the ratio of the times is 5:3.<br>
So the man spent 5/8 of the time at the lower rate and 3/8 of the time at the higher rate.<br>
Since the total time was 1 hour, he spent 5/8 of an hour at 3mph, traveling (5/8)*3 = 15/8 miles; and he spent 3/8 of an hour at 5mph, traveling (3/8)*5) = 15/8 miles.<br>
So the total distance he traveled is 15/8+15/8 = 15/4 miles.