A race is x miles long. If Henrik has run half as far as Lars, and Lars has run 3/4 of the race, how far have they run

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BTGmoderatorLU: Moderator; Posts: 2650; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Fri Apr 30, 2021 9:51 am

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Source: Veritas Prep

A race is x miles long. If Henrik has run half as far as Lars, and Lars has run 3/4 of the race, how far have they run collectively, in terms of x?

A. x/4
B. 4x/6
C. x
D. 5x/4
E. 9x/8

The OA is E

Source: Beat The GMAT — Problem Solving | Fri Apr 30, 2021 9:51 am

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

Re: A race is x miles long. If Henrik has run half as far as Lars, and Lars has run 3/4 of the race, how far have they r

by swerve » Fri Apr 30, 2021 2:52 pm

BTGmoderatorLU wrote: ↑
Fri Apr 30, 2021 9:51 am
Source: Veritas Prep

A race is x miles long. If Henrik has run half as far as Lars, and Lars has run 3/4 of the race, how far have they run collectively, in terms of x?

A. x/4
B. 4x/6
C. x
D. 5x/4
E. 9x/8

The OA is E

$H=\dfrac{1}{2}L$

$L=\dfrac{3}{4}x$ where $x$ is the mile distance

Distance covered by $H=\dfrac{1}{2}\dfrac{3}{4}x$

Collective distance, $H + L = \dfrac{3}{8}x+\dfrac{3}{4}x = \dfrac{3+6}{8}x=\dfrac{9}{8}x$

Therefore, E

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