James started from his home and drove eastwards at a constant speed. Exactly 90 minutes after James started from his

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E-GMAT

James started from his home and drove eastwards at a constant speed. Exactly 90 minutes after James started from his home, his brother Patrick started from the same point and drove in the same direction as James did at a different constant speed. Patrick overtook James exactly 90 minutes after Patrick started his journey, and then continued driving at the same speed for another 2 hours. By what percentage should Patrick reduce his speed, so that James could catch up with Patrick in exactly 8 hours after Patrick overtook James?

A. 25%
B. 33%
C. 50%
D. 67%
E. 75%

OA D

[swerve]

E-GMAT

James started from his home and drove eastwards at a constant speed. Exactly 90 minutes after James started from his home, his brother Patrick started from the same point and drove in the same direction as James did at a different constant speed. Patrick overtook James exactly 90 minutes after Patrick started his journey, and then continued driving at the same speed for another 2 hours. By what percentage should Patrick reduce his speed, so that James could catch up with Patrick in exactly 8 hours after Patrick overtook James?

A. 25%
B. 33%
C. 50%
D. 67%
E. 75%

OA D

Let \(p=P\)'s speed
\(\dfrac{p}{2}=J\)'s speed

\(x=\)fraction of \(p\) driven for last \(6\) hours

In the \(8\) hours after overtaking \(J,\)
\(P\) drives \(2p+6xp\) miles
while \(J\) drives \(8\cdot \dfrac{p}{2}\) miles
\(2p+6xp=4p \Longrightarrow x=\dfrac{1}{3}\)

\(P\) should reduce his speed by \(\dfrac{2}{3}=67\%\)

Therefore, D