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# Vinay and Phil are driving in separate cars to Los Angeles, both leavi

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Math Expert
Joined: 02 Sep 2009
Posts: 51072
Vinay and Phil are driving in separate cars to Los Angeles, both leavi  [#permalink]

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27 Jun 2018, 20:36
00:00

Difficulty:

35% (medium)

Question Stats:

73% (02:03) correct 27% (02:30) wrong based on 72 sessions

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Vinay and Phil are driving in separate cars to Los Angeles, both leaving from the same place and traveling along the same route. If Vinay leaves at 1 a.m. and travels at 40 miles per hour, and Phil leaves at 5 a.m. and travels at 50 miles per hour, at what time does Phil catch up to Vinay?

A. 1 p.m.
B. 5 p.m.
C. 7 p.m.
D. 9 p.m.
E. 11 p.m.

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Joined: 04 Jan 2015
Posts: 2269
Re: Vinay and Phil are driving in separate cars to Los Angeles, both leavi  [#permalink]

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27 Jun 2018, 21:57
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Solution

Given:
• Vinay and Phil are driving in separate cars to Los Angeles, both leaving from the same place and traveling along the same route
• Vinay leaves at 1 a.m. and travels at 40 miles per hour
• Phil leaves at 5 a.m. and travels at 50 miles per hour

To find:
• The time at which Phil catches up Vinay

Approach and Working:
When Phil started journey, Vinay already travelled for 4 hours
• Hence, at 5 a.m., the distance between Phil and Vinay = 40 * 4 = 160 miles

5 a.m. onwards Vinay moved at 40 mph and Phil moved at 50 mph, at the same direction
• So, in 1-hour time, the distance between them getting reduced by (50 – 40) = 10 miles

Therefore, to reduce the gap of 160 miles, they will take = $$\frac{160}{10}$$ = 16 hours
• So, they will meet 16 hours from 5 a.m., or at 9 p.m.

Hence, the correct answer is option D.

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Re: Vinay and Phil are driving in separate cars to Los Angeles, both leavi  [#permalink]

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28 Jun 2018, 11:54
Vinay's distance covered before Phil started = 40*4 = 160 miles.
Let time taken by Phil to catch up Vinay be x.
Then, 50x = 40x + 160, x = 16.
Hence, time at which Phil was able to catch up = 5 a.m. + 16 = 9 p.m.
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: Vinay and Phil are driving in separate cars to Los Angeles, both leavi  [#permalink]

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02 Jul 2018, 08:38
Bunuel wrote:
Vinay and Phil are driving in separate cars to Los Angeles, both leaving from the same place and traveling along the same route. If Vinay leaves at 1 a.m. and travels at 40 miles per hour, and Phil leaves at 5 a.m. and travels at 50 miles per hour, at what time does Phil catch up to Vinay?

A. 1 p.m.
B. 5 p.m.
C. 7 p.m.
D. 9 p.m.
E. 11 p.m.

We can let Vinay’s time = t + 4 and Phil's time = t and create the equation:

Distance of Vinay = Distance of Phil

40(t + 4) = 50t

40t + 160 = 50t

160 = 10t

16 = t

Phil catches up to Vinay at 5 am + 16 hours = 9 pm.

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Re: Vinay and Phil are driving in separate cars to Los Angeles, both leavi &nbs [#permalink] 02 Jul 2018, 08:38
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