You may find it easier if you let each leg = 4 (lengths don't matter here, so use an easy one!);

then 3/4 lengths become 4 + 4 + 1 and 1 + 4 + 4; using u,v,w as speeds (as Earboth did),

you can then work with these:

Code:

4/u + 4/v + 1/w = 7/2 [1]
1/u + 4/v + 4/w = 9/2 [2]
-4/u + 4/v = 1/6 [3]

Using elimination, you get rid of the w's first:

say multiply [1] by -4, then add to [2]; will leave:

15/u + 12/v = 19/2 [4]

Similarly, eliminate v's using [3] and [4]:

say multiply [3] by -3, then add to [4]; will leave:

27/u = 9

u = 3

Substitute back, and you'll end up with v = 8/3 and w = 3/2.

Since total time is 4/u + 4/v + 4/w, then:

total time = 4/3 + 4/(8/3) + 4/(3/2) = 5.5 (as Earboth got).