Question 152437
Suppose you swam at x miles per hour.
Then you ran at 2x miles per hour, and cycled at 3x miles per hour.

Time spent on swimming: 3/x
Time spent on running: 5/(2x)
Time spent on cycling: 10/(3x)

The total time spent is: 3/x + 5/(2x) + 10/(3x)

As the total time was one hour and forty-six minutes, we can set up an equation:
3/x + 5/(2x) + 10/(3x) = 1 + 46/60
Solving for x, we have
18/(6x) + 15/(6x) + 20/(6x) = 53/30
53/(6x) = 53/30
1/(6x) = 1/30
6x = 30
x = 5
So he swam at 5 miles per hour.