Problems(2)
Three runners start running simultaneously from the same point on a 500-meter circular track. They each run clockwise around the course maintaining constant speeds of 4.4, 4.8, and 5.0 meters per second. The runners stop once they are all together again somewhere on the circular course. How many seconds do the runners run?<spanclass=′latex−bold′>(A)</span> 1,000<spanclass=′latex−bold′>(B)</span> 1,250<spanclass=′latex−bold′>(C)</span> 2,500<spanclass=′latex−bold′>(D)</span> 5,000<spanclass=′latex−bold′>(E)</span> 10,000 modular arithmeticAMC
Three circles with radius 2 are mutually tangent. What is the total area of the circles and the region bounded by them, as shown in the figure? [asy]
filldraw((0,0)--(2,0)--(1,sqrt(3))--cycle,gray,gray);
filldraw(circle((1,sqrt(3)),1),gray);
filldraw(circle((0,0),1),gray);
filldraw(circle((2,0),1),grey);
[/asy]<spanclass=′latex−bold′>(A)</span> 10π+43<spanclass=′latex−bold′>(B)</span> 13π−3<spanclass=′latex−bold′>(C)</span> 12π+3<spanclass=′latex−bold′>(D)</span> 10π+9<spanclass=′latex−bold′>(E)</span> 13π geometryAMC