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

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

by Max@Math Revolution » Wed May 02, 2018 1:54 am

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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. (1/3)x
B. (1/2)x
C. x
D. 2x
E. 3x
Last edited by Max@Math Revolution on Thu May 03, 2018 11:14 am, edited 1 time in total.
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by GMATGuruNY » Wed May 02, 2018 2:50 am
Max@Math Revolution 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. (1/3)x
B. (1/2)x
C. x
D. 2x
E. 3x
Total distance between Alice and Bob =120 miles.
Since Alice travels 40 miles from her home to meet Bob, Bob travels the remaining 80 miles.
Since Bob travels twice as far as Alice, his rate is twice Alice's rate.
Since Alice's rate = x miles per hour, Bob's rate = 2x miles per hour.

The correct answer is D.

Alternate approach:

As noted above:
Total distance between Alice and Bob =120 miles.
Since Alice travels 40 miles from her home to meet Bob, Bob travels the remaining 80 miles.

Let x=40, implying that Alice's rate = 40 mph.
Since Alice's rate = 40 mph, the time for her to travel 40 miles from her home to meet Bob = d/r = 40/40 = 1 hour.
In this same 1 hour, Bob travels the remaining 80 miles from his home to meet Alice, implying that Bob's rate = d/t = 80/1 = 80 mph.

The question stem asks for Bob's rate: 80 mph.
Now plug x=40 into the answers to see which yields the target value of 80.
Only D works:
2x = 2*40 = 80.
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by Brent@GMATPrepNow » Wed May 02, 2018 10:43 am
The correct answer is showing up as B
Upon re-reading the question, we can see that it's somewhat 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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by Jeff@TargetTestPrep » Thu May 03, 2018 3:27 pm
Max@Math Revolution 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. (1/3)x
B. (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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by Max@Math Revolution » Thu May 03, 2018 11:34 pm
=>

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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by deloitte247 » Mon May 07, 2018 10:10 am
The duo met 40miles away from Alice house.
Alice has covered distance of 40miles
Bob has cover distance of 120-40
= 80miles
Alice velocity = x miles per hour
Given that they met at some time but cover different distance means their velocity id different.
Bob cover's most of the distance, this means Bob's velocity is twice that of Alice to cover twice the distance Alice was able to cover (40
: 80)
$$\frac{40}{x\ }\ =\ \frac{80}{y}$$
$$\frac{40y}{40}\ =\ \frac{80x}{40}$$
y = 2x
Option D is the correct answer
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