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# Judy drove 20 miles from her house to a theater at an average rate of

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Math Expert
Joined: 02 Sep 2009
Posts: 65768
Judy drove 20 miles from her house to a theater at an average rate of  [#permalink]

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07 Nov 2018, 22:53
00:00

Difficulty:

25% (medium)

Question Stats:

77% (01:59) correct 23% (02:19) wrong based on 115 sessions

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Judy drove 20 miles from her house to a theater at an average rate of 50 miles per hour. Greg drove from his house to the theater in $$\frac{1}{3}$$ of the time it took Judy to drive to the theater, and they both arrived at the theater at the same time. If Judy left her house at 7:30 P.M., when did Greg leave his house?

A. 7:34 P.M.

B. 7:38 P.M.

C. 7:42 P.M.

D. 7:46 P.M.

E. 7:54 P.M.

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Joined: 08 Sep 2008
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Concentration: Operations, General Management
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Re: Judy drove 20 miles from her house to a theater at an average rate of  [#permalink]

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07 Nov 2018, 23:01
Judy: Time taken = Distance/ Speed = 20/50 =0.4 hrs = 24 minutes.

Judy left her house: 7:30 PM --- reached Theater -- 7:54 PM

Greg took 1/3 time i.e. Greg took 24/3=8 minutes.

Greg left home at 7:54 PM- ( 8 Minutes)= 7:46 PM

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Re: Judy drove 20 miles from her house to a theater at an average rate of  [#permalink]

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07 Nov 2018, 23:17
Bunuel wrote:
Judy drove 20 miles from her house to a theater at an average rate of 50 miles per hour. Greg drove from his house to the theater in $$\frac{1}{3}$$ of the time it took Judy to drive to the theater, and they both arrived at the theater at the same time. If Judy left her house at 7:30 P.M., when did Greg leave his house?

A. 7:34 P.M.

B. 7:38 P.M.

C. 7:42 P.M.

D. 7:46 P.M.

E. 7:54 P.M.

Time = distance/speed = 20/50 = 2/5

2/5 * 60 = 24 minutes if judy left 7:30 and arrived at 7:54

1/3 of the time = 1/3 * 24 = 8 minutes.

It means he left at 7:46

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Joined: 04 Jan 2015
Posts: 3440
Re: Judy drove 20 miles from her house to a theater at an average rate of  [#permalink]

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29 May 2020, 08:20

Solution

Given
In this question, we are given that
• Judy drove 20 miles from her house to a theater at an average rate of 50 miles per hour
• Greg drove from his house to the theater in 1/3 of the time it took Judy to drive to the theatre
• They both arrived at the theater at the same time
• Judy left her house at 7:30 P.M.

To find
We need to determine
• The time at which Greg left his house

Approach and Working out
At a speed of 50 miles per hour, Judy takes 20/50 hours or 24 minutes to reach theatre.
• As Judy started at 7:30 pm, Judy would have reached at 7:54 pm

Also, Greg travelled for 1/3rd of the time that Judy travelled
• Hence, Greg travelled for (1/3 x 24) minutes or 8 minutes

As Greg also reached theatre at 7:54 pm by travelling for 8 minutes,
• Greg must have started at 7:46 pm

Thus, option D is the correct answer.

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Re: Judy drove 20 miles from her house to a theater at an average rate of   [#permalink] 29 May 2020, 08:20