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Two cars A and B start from Boston and New York respectively [#permalink]
13 Mar 2005, 09:19

Two cars A and B start from Boston and New York respectively simultaneously and travel towards each other at constant speeds. After meeting at a point between Boston and New York the two cars A and B proceed to their respective destinations of New York and Boston. Car A reaches New York 40 minutes after the two cars have met and Car B reaches Boston 90 minutes after they have met. How long did Car A take to cover the distance between Boston and New York?

A. 1 hour
B. 1 hour 10 minutes
C. 2 hours 30 minutes
D. 1 hour 40 minutes
E. 2 hours 10 minutes

With the information given, you can compute the ratio of the rates r1:r2 as 3:2, where r1 is the rate of A and r2 is the rate of B. You also can deduce that it takes 1 hr for them to meet by picking numbers, if the total distance is 50, with the above ratio the 2 will meet after 1 hour and this is true for any distance between Boston and New York if the relative ratios are known. Further, A travels an additional 40 mins, so A travels a total of 100 mins or 1hr 40 mins.

The time they both travel at the point they meet are equal:
d=rt
(distance traveled by b at the meeting pt) / time it take A to cover that distance = rate of A or r1

r2.t = dist. traveled by b. r2t/(2/3) = r1 ; t = (2/3)*(r1/r2)
Similarly, t is also equal to (3/2)*(r2/r1), from here, you can calc the ratio of r1:r2 as 3:2.