Next-door neighbors bob and jim use hoses from both houses to fill bob's swimming pool. they
know that it takes 18 hours using both hoses. they also know that bob's hose, used alone, takes 20%
less time than jim's hose alone. how much time is required to fill the pool by each hose alone?

Here is their argument. given the obtuse angle x, we make a quadrilateral abcd with ∠dab = x, and ∠abc = 90◦, and ad = bc. say the perpendicular bisector to dc meets the perpendicular bisector to ab at p. then pa = pb and pc = pd. so the triangles pad and pbc have equal sides and are congruent. thus ∠pad = ∠pbc. but pab is isosceles, hence ∠pab = ∠pba. subtracting, gives x = ∠pad−∠pab = ∠pbc −∠pba = 90◦. this is a preposterous conclusion – just where is the mistake in the "proof" and why does the argument break down there?

What is the solution to the equation? k/6.4=8.7 2.3 5.568 15.1 55.68

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