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The distance between Alice’s house and Bob's is 120 miles. Alice and B

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The distance between Alice’s house and Bob's is 120 miles. Alice and B  [#permalink]

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New post Updated on: 03 May 2018, 11:09
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[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?

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

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Originally posted by MathRevolution on 02 May 2018, 02:03.
Last edited by MathRevolution on 03 May 2018, 11:09, edited 1 time in total.
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Re: The distance between Alice’s house and Bob's is 120 miles. Alice and B  [#permalink]

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New post 02 May 2018, 06:15
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.
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Re: The distance between Alice’s house and Bob's is 120 miles. Alice and B  [#permalink]

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New post 02 May 2018, 06:21
MathRevolution wrote:
[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?

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


Dear MathRevolution,
If they met 40 miles from Alice house, so A walked 40 miles and Bob 80 miles. The time is the same, so

40/x = 80/y
y=2x
Answer (D)

Please check OA. Logicaly Bob's speed can not be twice slower than Alice's, otherwise they would met closer to Bob's house.
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Re: The distance between Alice’s house and Bob's is 120 miles. Alice and B  [#permalink]

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New post 02 May 2018, 10:45
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Top Contributor
ocelot22 wrote:
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.

Cheers,
Brent
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Re: The distance between Alice’s house and Bob's is 120 miles. Alice and B  [#permalink]

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New post 02 May 2018, 13:08
i got this wrong. Might have missed out on something
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Re: The distance between Alice’s house and Bob's is 120 miles. Alice and B  [#permalink]

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New post 02 May 2018, 13:13
Top Contributor
saraheja wrote:
i got this wrong. Might have missed out on something


See my post above yours.
The question is ambiguous.

Cheers,
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Re: The distance between Alice’s house and Bob's is 120 miles. Alice and B  [#permalink]

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New post 02 May 2018, 15:18
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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Re: The distance between Alice’s house and Bob's is 120 miles. Alice and B  [#permalink]

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New post 03 May 2018, 15:23
MathRevolution wrote:

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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Re: The distance between Alice’s house and Bob's is 120 miles. Alice and B  [#permalink]

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New post 06 May 2018, 06:19
=>

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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Re: The distance between Alice’s house and Bob's is 120 miles. Alice and B  [#permalink]

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New post 07 May 2018, 03:49
MathRevolution wrote:
[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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Re: The distance between Alice’s house and Bob's is 120 miles. Alice and B  [#permalink]

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Re: The distance between Alice’s house and Bob's is 120 miles. Alice and B   [#permalink] 30 May 2020, 15:07

The distance between Alice’s house and Bob's is 120 miles. Alice and B

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