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At 9 am, Amy started driving from her house towards north at a speed..

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At 9 am, Amy started driving from her house towards north at a speed..  [#permalink]

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New post 21 Nov 2018, 04:01
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A
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D
E

Difficulty:

  55% (hard)

Question Stats:

70% (01:47) correct 30% (02:08) wrong based on 54 sessions

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At 9 am, Amy started driving from her house towards north at a speed of 60 mph. Amy’s brother Bernie started from the same place, in his car, at 11:30 am and drove towards south at a speed of 90 mph. If at a certain point of time, the distance between them is 600 miles, then at what time was this distance measured?

    A. 1 pm
    B. 1: 30 pm
    C. 2 pm
    D. 2: 30 pm
    E. 3 pm

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Re: At 9 am, Amy started driving from her house towards north at a speed..  [#permalink]

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New post 21 Nov 2018, 04:07
Amy and Bernie started from the same place.
Amy started at 9 am, by 11:30 am, Amy would have covered 150 miles at 60mph.
Bernie starts at 11:30 am and moves towards the south.
After every 1 hour, the distance between them increases by 90+60 miles = 150 miles.
At 12:30 pm, the distance would be 300 miles.

Then for the distance between them to be 600 miles. It would take another 2 hours. Hence at 2:30 PM, distance between Amy and Bernie would be 600 miles.

D is the answer.
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Re: At 9 am, Amy started driving from her house towards north at a speed..  [#permalink]

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New post 21 Nov 2018, 04:08
Amy speed 60mph
Bernie speed 90 mph

Distance covered by amy till 11:30 (i.e. 2.5 hrs) =150 miles.

@1130 relative speed between amy and Bernie is 60+90 =150mph
Distance remaining between two of them at 1130 = 600-150=450 miles

Time required to cover this 450 miles@150mph= 3 hrs

So at 1130 +3 hrs 2:30 PM distance will be 600 miles.

Answer D.
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Re: At 9 am, Amy started driving from her house towards north at a speed..  [#permalink]

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New post 23 Nov 2018, 06:15

Solution



Given:
    • Amy started her journey, at 9 am, towards north at a speed of 60mph
    • Bernie started his journey, at 11:30 am, towards south at a speed of 90 mph

To find:
    • Time at which the distance between them is 600 miles

Approach and Working:
    • Let us assume that Amy has travelled for T hours till that point
      o Implies, Bernie has travelled for T – 2.5 hours

Now, let’s represent all the given information in a DST table
Image

    • We know that, x + y = 600
      o Implies, 60 * T + 90 * (T – 2.5) = 600
      o Thus, T = \(\frac{11}{2}\) hours
    • Therefore, time at which the distance between them is 600 miles = 9 am + 5.5 hours = 2:30 pm

Hence the correct answer is Option D.

Answer: D
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Re: At 9 am, Amy started driving from her house towards north at a speed.. &nbs [#permalink] 23 Nov 2018, 06:15
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