If we let D?, r?, and t? denote the variables for the Clarke family's trip and D?, r?, and t? denote the variables for the Rourke family's trip, we see that:
D? = r?t? and D? = r?t?.
We see that from the problem, r? = 6, t? = t?, r? = 14, and D? = D? + 20. Then:
D? = 6t? and D? + 20 = 14t?
==> D? = 6t? and D? = 14t? - 20.
Setting these equations equal yields:
6t? = 14t? - 20
==> 8t? = 20
==> t? = 20/8 = 2.5 hours.
So each family spent 2.5 hours on their boat trip. <== ANSWER
As a check, we see that the first family traveled (2.5)(6) = 15 km while the second family traveled (2.5)(14) = 35 km, which is 20 km more than the first trip as required.
I hope this helps!