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# Alice drives her car from town M to town N at a constant rate of 35 mi

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Math Revolution GMAT Instructor
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Alice drives her car from town M to town N at a constant rate of 35 mi [#permalink]

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22 Dec 2017, 05:48
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Question Stats:

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[GMAT math practice question]

Alice drives her car from town M to town N at a constant rate of 35 miles per hour. One hour after Alice sets out, Bob starts to drive from town N to town M along the same road at a constant rate of 45 miles per hour. If the distance between towns M and N is 355 miles, then what distance in miles has Alice traveled when she and Bob pass each other?

A. 70 miles
B. 105 miles
C. 140 miles
D. 175 miles
E. 210 miles
[Reveal] Spoiler: OA

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Re: Alice drives her car from town M to town N at a constant rate of 35 mi [#permalink]

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22 Dec 2017, 08:16
MathRevolution wrote:
[GMAT math practice question]

Alice drives her car from town M to town N at a constant rate of 35 miles per hour. One hour after Alice sets out, Bob starts to drive from town N to town M along the same road at a constant rate of 45 miles per hour. If the distance between towns M and N is 355 miles, then what distance in miles has Alice traveled when she and Bob pass each other?

A. 70 miles
B. 105 miles
C. 140 miles
D. 175 miles
E. 210 miles

Distance traveled by Alice during the first 1 hour $$= 35*1=35$$

Now Bob start from opposite direction, Hence relative speed of these two will be $$= 35+45=80$$

Distance left to be covered before Alice crosses Bob$$= 355-35=320$$

Time take to cross Bob $$= \frac{320}{80}=4$$ hours

So distance traveled by Alice when she crosses Bob $$= 35+4*35= 175$$ miles

Option D
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Alice drives her car from town M to town N at a constant rate of 35 mi [#permalink]

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22 Dec 2017, 08:28
MathRevolution wrote:
[GMAT math practice question]

Alice drives her car from town M to town N at a constant rate of 35 miles per hour. One hour after Alice sets out, Bob starts to drive from town N to town M along the same road at a constant rate of 45 miles per hour. If the distance between towns M and N is 355 miles, then what distance in miles has Alice traveled when she and Bob pass each other?

A. 70 miles
B. 105 miles
C. 140 miles
D. 175 miles
E. 210 miles

Closing the "gap" when travelers start at different times and travel in opposite directions. Original distance = 355 miles

1) Alice starts first and changes the distance:
For one hour at 35 mph, she drives 35 miles
New distance between them: (355-35)= 320 miles

2) When Bob starts, the gap between them will close faster than when just one drives.
Add speeds. Combined rate is (35+45)= 80 mph

3) TIME they travel before they pass each other, D/r= t, $$\frac{320}{80} = 4$$
hrs

4) Total miles Alice traveled?
One hour alone + 4 hrs while both drive:
5 hours * 35 mph = 175 miles

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Re: Alice drives her car from town M to town N at a constant rate of 35 mi [#permalink]

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25 Dec 2017, 17:06
=>
After 1 hour, Alice has traveled 35 miles. So, the distance between Alice and Bob is 320 miles. Alice and Bob approach each other at a speed of 35 + 45 = 80 miles per hour. They pass each other after 320/80 = 4 hours. Thus, when they pass each other, Alice has been driving for 1 + 4 = 5 hours. The total distance she has traveled is 5 x 35 = 175 miles.

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Re: Alice drives her car from town M to town N at a constant rate of 35 mi   [#permalink] 25 Dec 2017, 17:06
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