Bunuel wrote:
vdadwal 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?
A. 1 hour
B. 1 hour 10 minutes
C. 2 hours 30 minutes
D. 1 hour 40 minutes
E. 2 hours 10 minutes
Look at the diagram below:
Attachment:
The attachment Boston - New York.png is no longer available
The rate of car A is \(a\) and the rate of B is \(b\);
The distance covered by A before the meeting point is \(x\) and the distance covered by B before the meeting point is \(y\);
Time before meeting \(t\).
Since car A covered the distance of \(y\) in 40 minutes then the rate of car A = distance/time = \(a=\frac{y}{40}\), but the same distance of \(y\) was covered by car B in \(t\) minutes, so \(y=bt\) --> \(a=\frac{bt}{40}\);
Since car B covered the distance of \(x\) in 90 minutes then the rate of car B = distance/time = \(b=\frac{x}{90}\), but the same distance of \(x\) was covered by car A in \(t\) minutes, so \(x=at\) --> \(b=\frac{at}{90}\);
Substitute \(b\) in the first equation: \(a=\frac{at}{90}*\frac{t}{40}\) --> reduce by \(a\) and cross-multiply: \(t^2=3600\) --> \(t=60\) minutes, hence it took car A 60+40=100 minutes to cover the whole distance.
Answer: D.
Hope it's clear.
I have solved using a different approach and am getting E as the answer, can you please let me know what have I done wrong
Assume total distance = d
Assume total time = t
Assume distance covered by A by the time it meets B = kd
kd is covered in (t-40) min by A and in 90 min by B
Similarly the remaining distance covered by A will be (1-k)d which is covered in 40 min
The same distance (1-k)d will be covered by B in (t-90) min
Now, because the rate is constant for A for the entire distance and similarly for B
I came up with below eqns
kd/(t-40) = (1-k)d/40
(1-k)d/(t-90) = kd/90
On solving these equations, I am getting 2hr 10 min as the answer
Can you please help
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