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Rachel and Rob live 190 miles apart. They both drive in a straight lin

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Rachel and Rob live 190 miles apart. They both drive in a straight lin  [#permalink]

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New post 05 Feb 2019, 03:01
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A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

61% (02:34) correct 39% (02:11) wrong based on 66 sessions

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Re: Rachel and Rob live 190 miles apart. They both drive in a straight lin  [#permalink]

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New post 05 Feb 2019, 04:44
2
IMO D.

D = 190
Relative speed S = 70+50=120
Time when Rachel and Rob meet T = 190/120= 19/12 hours

45 minutes before they meet can be represented as, T - 3/4 hours = 19/12 - 3/4 = 5/6 hours

distance covered by Rachel 45 min before she meets Rob = 50*5/6
distance covered by Rob 45 min before he meets Rachel = 70*5/6
Total distance covered by Rachel and Rob when they meet each other = 50*5/6 + 70*5/6 = 5/6*120 = 100 miles

So Rachel and Rob will be 190-100= 90 miles apart 45 mins before they meet.

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Re: Rachel and Rob live 190 miles apart. They both drive in a straight lin  [#permalink]

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New post 05 Feb 2019, 04:51
Bunuel wrote:
Rachel and Rob live 190 miles apart. They both drive in a straight line toward each other to meet for tea. If Rachel drives at 50 mph and Rob drives at 70 mph, then how many miles apart will they be exactly 45 minutes before they meet?

A. 50
B. 60
C. 70
D. 90
E. 100



total relative speed = 50+70 = 120 mph
distance = 190 miles
so total time they would take = 190/120 = 1.58 hours
45 mins = 45/60 = 0.75 hrs
so before 0.75 hrs they both have travelled for 1.58-0.75 = 0.83 hrs
distance travelled by Rachel = 0.83 * 50 = 41.5 miles and rob = 0.83 * 70 = 58.1
total distance = 99.6 ~100 miles
so they are 190-100 = 90 miles apart
IMO D
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Re: Rachel and Rob live 190 miles apart. They both drive in a straight lin  [#permalink]

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New post 07 Feb 2019, 19:42
Bunuel wrote:
Rachel and Rob live 190 miles apart. They both drive in a straight line toward each other to meet for tea. If Rachel drives at 50 mph and Rob drives at 70 mph, then how many miles apart will they be exactly 45 minutes before they meet?

A. 50
B. 60
C. 70
D. 90
E. 100


We can let t = the time if takes to meet and create the equation:

50t + 70t = 190

120t = 190

t = 190/120 = 19/12 hours or 19/12 x 60 = 95 minutes

So each will have driven for 50 minutes when it is 45 minutes before they meet. Therefore, together they will have driven (50 + 70) x 50/60 = 120 x 50/60 = 2 x 50 = 100 miles. Since the total distance is 190 miles, they will be 190 - 100 = 90 miles apart when it is exactly 45 minutes before they meet.

Alternate solution:

Notice that the distance between the two decreases by 50 + 70 = 120 miles every hour. Since they have to drive 45 more minutes to meet when it is exactly 45 minutes before they meet, they must be (50 + 70) x 45/60 = 120 x 45/60 = 2 x 45 = 90 miles apart.

Answer: D
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Re: Rachel and Rob live 190 miles apart. They both drive in a straight lin  [#permalink]

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New post 26 Feb 2019, 20:30
Let X be meeting point.
Rob------------------------------------X-------------------------------------------Rachel

45 mins prior to meeting point, Rachel would have travelled (3/4 * 50) miles from right of X to X
and Rob would have travelled (3/4 * 70) miles from left of X to X.

so distance apart = (3/4) * 50 + (3/4) * 70 = (3/4) * 120 = 90 miles
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Re: Rachel and Rob live 190 miles apart. They both drive in a straight lin   [#permalink] 26 Feb 2019, 20:30
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