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This is what i am getting alice's distance = 40mi alice's rate = x mi/hr --> Alice's time which must equal Bob's time = 40/x
Bob's distance must = 80 Mi Bobs rate then must be 80/40/x=2x? I must be missing something.

You're not missing anything.

The question is ambiguous because it doesn't specify where Alice and Bob are when they begin their journeys (although I also assumed that Alice started at her own house and Bob started at his own house).

If each person started at his/her own house (and started walking to the other person's house), then the correct answer is D.
If each person started at the OTHER person's house (and started walking home), then the correct answer is B.

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i got this wrong. Might have missed out on something
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i got this wrong. Might have missed out on something

See my post above yours.
The question is ambiguous.

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Point of start is not mentioned here.
Conventionally, we can assume that both start to walk from their own houses at same time in opposite direction on same road.
Thus, answer is D.
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The distance between Alice’s house and Bob's is 120 miles. Alice and Bob travel in opposite directions along the same road, starting at the same time. They meet at a place that is 40 miles away from Alice’s house. If Alice’s velocity is x miles per hour, what is Bob's velocity in terms of x?

\(A. (\frac{1}{3})x\)
\(B. (\frac{1}{2})x\)
\(C. x\)
\(D. 2x\)
\(E. 3x\)

The distance between Alice’s house and Bob's is 120 miles, and the meeting place is 40 miles away from Alice’s house. Therefore, Alice must have traveled 40 miles, and Bob must have traveled 80 miles. We see that Bob has traveled twice the distance Alice has traveled. Since they start at the same time, Bob must be traveling twice as fast as Alice in order to cover the distance that is twice as long. Since we are given that Alice is traveling at x mph, Bob must be traveling at 2x mph.

Answer: D
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=>

Let v be Bob’s speed, and let t be the time they take to reach their meeting point. Then
xt = 40 and vt = 120 – 40 = 80.

Bob travels 80 miles in the time it takes Alice to travel 40 miles.
Thus, Bob’s speed is twice Alice’s speed.
In terms of x, this is 2x.

Therefore, the answer is D.

Answer : D
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MathRevolution
[GMAT math practice question]

The distance between Alice’s house and Bob's is 120 miles. Alice and Bob travel in opposite directions along the same road, starting at the same time. They meet at a place that is 40 miles away from Alice’s house. If Alice’s velocity is x miles per hour, what is Bob's velocity in terms of x?

\(A. (\frac{1}{3})x\)
\(B. (\frac{1}{2})x\)
\(C. x\)
\(D. 2x\)
\(E. 3x\)

distance traveled in time is in ration 1:2 , so speed during that time would also be in ration 1:2 or x:2x

hence, d.
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