# Math problem help please: boating on a lake?

the clarke family went sailing on a lake. their boat averaged 6 kilometers per hour. the rourke family took their outboard runabout for a trip on the lake for the same amount of time. their boat averaged 14 kilometers per hour. the rourke family traveled 20 kilometers farther than the clarke family. how many hours did each family spend on their boat trip?

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!

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