LUANDATO wrote:Frank and georgia started traveling from A to B at the same time. Georgia's constant speed was 1.5 times Frank's constant speed. When Georgia arrived at B, she turned right around and returned by the same route. She cross paths with Frank, who still was coming toward B, when they were 60 miles away from B. How far away are A and B?
A. 72 miles
B. 120 miles
C. 144 miles
D. 240 miles
E. 300 miles
Let d = the distance between A and B.
Georgia travels the total distance in red:
A------------------------------------------->B
A................................................<-----60-----B
Since Georgia travels the distance between A and B plus an additional 60 miles, Georgia's distance = d+60.
Frank travels the distance in blue:
A----------------------------->.........60.........B
Since Frank travels the distance between A and B except for the last 60 miles, Frank's distance = d-60.
Since Georgia's rate is 3/2 Frank's rate -- and the two travel for the same amount of time -- Georgia's distance must be 3/2 Frank's distance:
d+60 = (3/2)(d-60)
2d + 120 = 3(d-60)
2d + 120 = 3d - 180
300 = d.
The correct answer is
E.
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