Two circles, one with radius 10 inches and the other with radius 4 inches, are tangent at point A. Two insects start crawling at the same time from point A: one along the larger circle at 3π inches per minute, the other along the smaller circle at 2.5π inches per minute. How much time has elapsed when the two insects meet again at point A?
Select the correct option
A) 15 minutes	B) 30 minutes	C) 40 minutes	D) 1 hour	E) 1 hour, 20 minutes
First we figure out the circumference of the circles so we can determine how long it takes to complete one revolution from point A to point A .   C (large) = 20pi   C (small) = 8pi   R (large) = 3pi   R (small) = 5/2pi   It takes 20/3 minutes to make one revolution around the larger circle   It takes 8/(5/2) = 16/5 minutes to make one revolution around the smaller circle   The time it takes them to intersect can be determined by finding the LCM of both times. Get the denominators of both numbers equal one another.   20/3 = 100/15   16/5 = 48/15   LCM of 48 and 100:   48 = 2*2*2*2*3   100 = 2*2*5*5   LCM = 2*2*2*2*3*5*5= 
<gadget id="calculator">2*2*2*2*3*5*5</gadget>
<output>1_200</output>
1200   1200/15= 
<gadget id="calculator">1200/15</gadget>
<output>80</output>
80 minutes.   (1 hour, 20 minutes) 1 hour, 20 minutes
<result>E</result>
Two circles, one with radius 10 inches and the other with radius 4 inches, are tangent at point A. Two insects start crawling at the same time from point A: one along the larger circle at 3π inches per minute, the other along the smaller circle at 2.5π inches per minute. How much time has elapsed when the two insects meet again at point A?