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

[BTGmoderatorLU]

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

[swerve]

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