Data Sufficiency

Exactly one straight road connects Albertville and Bowton, which are 90 miles apart. If Sierra leaves Albertville headed for Bowton at the same time that Dylan leaves Bowton headed for Albertville, and each travels along the road at a constant rate, how far will Sierra have traveled when they meet?

(1) Sierra travels at 3x miles per hour and Dylan travels at 4x miles per hour.
(2) Sierra travels at 5 miles per hour slower than Dylan does.


OA A

Source: Princeton Review

BTGmoderatorDC wrote: ↑

Tue Dec 01, 2020 5:52 pm

Exactly one straight road connects Albertville and Bowton, which are 90 miles apart. If Sierra leaves Albertville headed for Bowton at the same time that Dylan leaves Bowton headed for Albertville, and each travels along the road at a constant rate, how far will Sierra have traveled when they meet?

(1) Sierra travels at 3x miles per hour and Dylan travels at 4x miles per hour.
(2) Sierra travels at 5 miles per hour slower than Dylan does.


OA A

Source: Princeton Review

Distance covered by Sierra \(D_1= V_1\cdot T\)
Distance covered by Dylan \(D_2= V_2\cdot T\)

\(\dfrac{D_1}{D_2}= \dfrac{V_1}{V_2}\)

Statement 1:
\(\dfrac{V_1}{V_2} = \dfrac{3}{4}\)

\(\dfrac{D_1}{D_2}= \dfrac{3}{4}\)
\(\dfrac{D_1}{D_1+D_2}=\dfrac{3}{7}\)
\(D_1= 3\cdot \dfrac{90}{7}\)
Sufficient \(\Large{\color{green}\checkmark}\)

Statement 2:
Speed of Sierra \(= x-5\)
Speed of Dylan \(= x\)
\(\dfrac{D_1}{D_2}= X-\dfrac{5}{X}\)
Not sufficient \(\Large{\color{red}\chi}\)

Therefore, A