Two trains travel a 160 km track each day. The express travels 10 kmh faster and takes 30 minutes less time than the normal train. Find the speed of the express.

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 value of x? enter your answer in the box. x = in.

Petra is asked to color 6/6 on her grid she must use three colors blue red and pink there must be more blue section than red section are pink section what are the different ways peter can color of the