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

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AAPL: Moderator; Posts: 2749; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Thu Jul 01, 2021 9:57 am

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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

Source: Beat The GMAT — Problem Solving | Thu Jul 01, 2021 9:57 am

swerve: Legendary Member; Posts: 2604; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

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

by swerve » Fri Jul 02, 2021 7:10 am

AAPL wrote: ↑
Thu Jul 01, 2021 9:57 am
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

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