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Rachel and Rob live 190 miles apart. They both drive in a st [#permalink]
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Carcass 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 are they exactly 45 minutes before they meet?

A. 50

B. 60

C. 70

D. 90

E. 100

Kudos for the right answer and explanation


Since they are moving in the opposite direction (towards each other), their relative speed \(= 50 + 70 = 120mph\)

Time required to meet \(= \frac{190}{120} = 1.5833hours\) i.e. \(1\) hour \(35\) minutes

So \(45\) minutes before means, they travelled for \(50\) minutes

In \(50\) minutes, Rachel covered \(= (50)\frac{50}{60} = 41.667miles\) and Rob covered \(= (70)\frac{50}{60} = 58.333miles\)

Distance between them \(= 190 - 41.667 - 58.333 = 90miles\)

Hence, option D
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Rachel and Rob live 190 miles apart. They both drive in a st [#permalink]
Rachel ---------A ___________ B---------------Rob

As they drive in opposite direction, at 45min = 0.75hr before meeting, let's say that Rachel is at point A and Rob is at point B.
We know that they both meet after 45 mins which basically means that they both travelled distance AB in that last 45 mins.
So, AB = 50*0.75 + 70*0.75 = 90 miles
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Rachel and Rob live 190 miles apart. They both drive in a st [#permalink]
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distance, rate, time
190, 50+70=120mph, time
190, 120/60=2mpm, 95min
90, 2mpm, 45min

Simply 2 miles per minute x 45 minutes (distance to be covered) = 90
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Rachel and Rob live 190 miles apart. They both drive in a st [#permalink]
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I found my problem, I missed the word "before",

Hey everybody,
Why my approach provides a different answer?

Rachel - Speed: 50
Rob - Speed: 70

Total Speed: 120

They drove toward each other for 45 minutes (3/4 hours).

120x(3/4) = 90

They passed 90 miles together and the total distance was 190.
Therefore, they must still drive 100 miles to meet each other (190 - 90).
So the distance between them after 45 minutes is 100 miles.

Why doesn't my approach work?
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Rachel and Rob live 190 miles apart. They both drive in a st [#permalink]
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