Ann and Bea leave X-ville at the same time and travel towards Y-ville, which is

[BTGModeratorVI]

Ann and Bea leave X-ville at the same time and travel towards Y-ville, which is 70 kilometers away. Their individual speeds are constant, but Ann’s speed is greater than Bea’s speed. Upon reaching Y-ville, Ann immediately turns around and drives toward X-ville until she meets Bea. When they meet, how far has Bea traveled?

1) Ann’s speed is 30 kilometers per hour greater than Bea’s speed
2) Ann’s speed is twice Bea’s speed

Answer: B
Source: GMAT Prep Now

[Brent@GMATPrepNow]

Ann and Bea leave X-ville at the same time and travel towards Y-ville, which is 70 kilometers away. Their individual speeds are constant, but Ann’s speed is greater than Bea’s speed. Upon reaching Y-ville, Ann immediately turns around and drives toward X-ville until she meets Bea. When they meet, how far has Bea traveled?

1) Ann’s speed is 30 kilometers per hour greater than Bea’s speed
2) Ann’s speed is twice Bea’s speed

Answer: B
Source: GMAT Prep Now

Target question: When they meet, how far has Bea traveled?

Statement 1: Ann’s speed is 30 kilometers per hour greater than Bea’s speed
We can see that is not sufficient if we examine some EXTREME CASES:
Case a: Ann's speed = 30.00000001 kilometers per hour, and Bea's speed = 0.00000001 kilometers per hour. In this case, Bea travels almost 0 kilometers
Case b: Ann's speed = 40 kilometers per hour, and Bea's speed = 10 kilometers per hour. In this case, Bea travels more than 0 kilometers
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Ann’s speed is twice Bea’s speed
One option here is to test a bunch of cases to see what happens. If we do this, we'll find that we keep getting the same answer to the target question

Alternatively, we can use some algebra:
Let B = the distance Bea traveled
Let R = Bea's speed.

NOTE: the total distance from Townville to Villageton and then BACK TO Townville = 140 kilometers.

So, 140 - B = the distance Ann traveled
And 2R = Ann's speed (since her speed is TWICE Bea's speed)

From here, let's create a WORD EQUATION that uses distance and speed.
How about: Ann's travel time = Bea's travel time

Time = distance/rate, so we get:
(140 - B)/2R = B/R
Cross multiply to get: (B)(2R) = (R)(140 - B)
Expand: 2BR = 140R - BR
Add BR to both sides: 3BR = 140R
Divide both sides by R to get: 3B = 140
Divide both sides by 3 to get: B = 140/3
In other words, Bea traveled 140/3 kilometers
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

[deloitte247]

Given that: Distance from X-ville to Y-ville = 70km
Speeds are constant throughout the journey
Ann's speed > Bea's speed

Target question => When they meet, how far has Bea traveled?

Statement 1 => Ann's speed is 30km/hr greater than Bea's speed

Let distance traveled by Bea = x
Let Bea's speed = y
Let Ann's speed = (y + 30)km/hr
Let distance traveled by Ann on the journey back to X-ville = a

Total distance traveled by Ann = (70+a)km
Total distance traveled by Bea = (70-a)km

Ann's travel time =- Bea's travel time
$$where\ Ann's\ travel\ time=\frac{Ann's\ total\ dis\tan ce}{Ann's\ speed}=\frac{70+a}{y+30}$$
$$and\ Bea's\ time=\frac{Bea's\ total\ dis\tan ce}{Bea's\ speed}=\frac{70-a}{y}$$
$$\frac{70+a}{y+30}=\frac{70-a}{y}$$
$$y\left(70+a\right)=\left(y+30\right)\left(70-a\right)$$
$$70y+ay=70y-ay+2100-30a$$
$$ay+ay+30a=2100$$
$$2ay+30a=2100$$
$$\frac{2a\left(y+15\right)}{2}=\frac{2100}{2}$$
$$a\left(y+15\right)=1050$$
$$Value\ of\ a\ and\ y\ are\ unknown\ ,statement\ 1\ is\ NOT\ SUFFICIENT$$

Statement 2 => Ann's speed is twice Bea's speed
Let distance traveled by Ann on the journey back = a
Total distance traveled by Ann = (70+a)km
Total distance traveled by Bea = (70-a)km
Let Bea's speed = y
Ann's speed = 2y
Ann's travel time = Bea's travel time

$$\frac{70+a}{2y}=\frac{70-a}{y}$$
$$y\left(70+a\right)=2y\left(70-a\right)$$
$$70y+ay=140y-2ay$$
$$ay+2ay=140y-70y$$
$$\frac{3ay}{3y}=\frac{70y}{3y}$$
$$a=\frac{70}{3}$$
$$total\ dis\tan ce\ traveled\ by\ Bea\ =\ 70-a$$
$$where\ a\ =\frac{70}{3}$$
$$=70\ -\frac{70}{3}$$
$$=\frac{210-70}{3}=\frac{140}{3}=46.67km$$
$$Statement\ 2\ alone\ IS\ SUFFICIENT$$
$$Answer\ =\ B$$