Rachel drove the 120 miles from A to B at a constant speed. What was this speed?

[BTGmoderatorDC]

Rachel drove the 120 miles from A to B at a constant speed. What was this speed?

(1) If she had driven 50% faster, her new time would have by 2/3 of her original time.
(2) If she drove 20 mph faster, she would have arrived an hour sooner.


OA B

Source: Magoosh

[Brent@GMATPrepNow]

Rachel drove the 120 miles from A to B at a constant speed. What was this speed?

(1) If she had driven 50% faster, her new time would have by 2/3 of her original time.
(2) If she drove 20 mph faster, she would have arrived an hour sooner.


OA B

Source: Magoosh

Here's an algebraic solution for statement 2 that uses only 1 variable.

Target question: What was Rachel's speed?

Statement 1: If she had driven 50% faster, her new time would have been 2/3 of her original time.
Mitch has already done a great job (as usual) explaining why statement 1 is NOT SUFFICIENT, so I'll defer you to his solutions.

Statement 2: If she had driven 20 mph faster, she would have arrived an hour sooner.
Let's start with a "word equation"
When driving her regular speed, Rachel's trip time is 1 HOUR LONGER than her trip time when driving 20 mph faster.
So, let's write the following:
(Rachel's trip time at REGULAR speed) - (Rachel's trip time at FASTER speed) = 1 hour

From here, let's let R = her REGULAR speed
This means R + 20 = her FASTER speed

Since trip time = distance/speed, we can now write the following:
120/R - 120/(R+20) = 1 hour
Now solve the equation for R

Multiply both sides by (R)(R+20) to get: 120(R+20) - 120R = (R)(R+20)
Expand to get: 120R + 2400 - 120R = R² + 20R
Rearrange and simplify to get: R² + 20R - 2400 = 0
Factor: (R + 60)(R + 40) = 0
So, R = -60 or R = 40
Since Rachel's speed cannot be negative, it MUST be the case that R = 40
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

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Word problems are tricky for A LOT of students. One of the hardest steps is creating the corresponding equation(s). In many cases, I like to create a "WORD EQUATION" as an intermediary step.

Here's an article I wrote about this strategy: https://www.beatthegmat.com/mba/2014/09/ ... -equations

Here are a few questions where I've used a word equation:
- https://www.beatthegmat.com/insurance-t278612.html
- https://www.beatthegmat.com/equation-t107935.html
- https://www.beatthegmat.com/speed-distan ... 80473.html
- https://www.beatthegmat.com/stuck-with-m ... 63906.html
- https://www.beatthegmat.com/rate-distanc ... 21963.html
- https://www.beatthegmat.com/distance-wor ... 81078.html

Cheers,
Brent