amsm25 wrote:Two cars A and B start from Boston and New York respectively simultaneously and travel towards each other at constant speeds along the same route. 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?
1 hour
B. 1 hour 10 minutes
C. 2 hours 30 minutes
D. 1 hour 40 minutes
E. 2 hours 10 minutes
OA - D
Let us assume that the speed of car A = a and that of car B = b
Let the distance covered by car A before meeting at a point between Boston and New York = X
and the distance covered by car B before meeting at a point between Boston and New York = Y
Let the time before meeting = T
Now, car A covered the distance of X in 40 minutes, so speed of car A = distance/time
So, a = X/40
Also, distance of X was covered by car B in T minutes, so X = bt
So, a = bt/40 ... Equation 1
Car B covered the distance of Y in 90 minutes, so speed of car B = distance/time
So, b = Y/90
Also, distance of Y was covered by car A in T minutes, so Y = at
So, b = at/90 ... Equation 2
From equations 1 and 2, a = (at/90)t/40
a = (at/90) * (t/40)
t² = 3600
t = 60 minutes
Therefore, time taken by car A to cover the distance between Boston and New York = 60 + 40 = 100 minutes =
1 hour 40 minutes
The correct answer is D.
