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Both Robert and Alice leave from the same location at 7:00 a.m. drivin

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Bunuel
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Both Robert and Alice leave from the same location at 7:00 a.m. drivin [#permalink] New post   14 Feb 2020, 05:34
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Both Robert and Alice leave from the same location at 7:00 a.m. driving in the same direction, but in separate cars. Robert drives 30 miles per hour while Alice drives 40 miles per hour. After 6 hours, Alice’s car stops. At what time will Robert’s car reach Alice’s car?

A. 1 p.m.
B. 3 p.m.
C. 4 p.m.
D. 8 p.m.
E. 9 p.m.
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B
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Re: Both Robert and Alice leave from the same location at 7:00 a.m. drivin [#permalink] New post   14 Feb 2020, 06:53
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Bunuel wrote:
Both Robert and Alice leave from the same location at 7:00 a.m. driving in the same direction, but in separate cars. Robert drives 30 miles per hour while Alice drives 40 miles per hour. After 6 hours, Alice’s car stops. At what time will Robert’s car reach Alice’s car?

A. 1 p.m.
B. 3 p.m.
C. 4 p.m.
D. 8 p.m.
E. 9 p.m.


Robert Speed = 30
Alice Speed = 40

Relative Speed = 40-30 = 10 miles/hour

The distance between then in 6 hours (when Alice stops) = 10*6 = 60 miles

Time taken by Robert to reach Alice's car = 60/30 = 2 hours

i.e. (6 hours + 2 hours) from 7 AM

i.e. 3 PM

Answer: Option B
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Re: Both Robert and Alice leave from the same location at 7:00 a.m. drivin [#permalink] New post   14 Feb 2020, 23:37
total distance covered by Alice in 6 hrs ; 6*40 ; 240 miles
and distance covered by Robert in 6 hrs ; 6*30 ; 180 miles
net ∆ of distance; 60 miles which Robert at its speed will cover in 60/30 ; 2 hrs more
so time Alice had reached 240 miles ; 1PM and + 2 hrs ; 3 PM is time when Robert meets Alice
IMO B


Bunuel wrote:
Both Robert and Alice leave from the same location at 7:00 a.m. driving in the same direction, but in separate cars. Robert drives 30 miles per hour while Alice drives 40 miles per hour. After 6 hours, Alice’s car stops. At what time will Robert’s car reach Alice’s car?

A. 1 p.m.
B. 3 p.m.
C. 4 p.m.
D. 8 p.m.
E. 9 p.m.
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Both Robert and Alice leave from the same location at 7:00 a.m. drivin [#permalink] New post   18 Feb 2020, 05:16
Quote:
Both Robert and Alice leave from the same location at 7:00 a.m. driving in the same direction, but in separate cars. Robert drives 30 miles per hour while Alice drives 40 miles per hour. After 6 hours, Alice’s car stops. At what time will Robert’s car reach Alice’s car?

A. 1 p.m.
B. 3 p.m.
C. 4 p.m.
D. 8 p.m.
E. 9 p.m.



I can handle the 600-700 questions reliably at this point. Looking at this question, it's clear the distance (D) will be the same.
Knowing equation D=RT for both Alice and Robert, then --> RT (of Alice) = RT (of Robert).
Alice --- R=40, T=6
Robert --- R=30, T=6+X (X being the additional time driving)
40*6=30*(6+X) divide by 10 on both sides immediately to simplify numbers.
4*6=3*(6+X) dive by 3 on both sides to simplify numbers
4*2=6+X --> 8=6+X --> X=2

Since they started at 7am, and Alice drove for 6 hours, she stopped at 1pm. Robert drove for (2) more hours, and so stopped at 3pm.
Answer - B

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Re: Both Robert and Alice leave from the same location at 7:00 a.m. drivin [#permalink] New post   08 Jan 2023, 05:04
We can use ratios here for a quick solution as illustrated by Veritas prep Karishma

Ratios of
Speed of Robert/Speed of Alice = 30/40 = 3/4
Time By Robert/Time by Alice = 4/3 (Inverse of the ratio of Speed)

Time taken by Robert = 6*4/3 = 8

7.00 am + 8 hours = 3.00 pm

Ans. B
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Re: Both Robert and Alice leave from the same location at 7:00 a.m. drivin [#permalink]
08 Jan 2023, 05:04
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