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vladmire: Master | Next Rank: 500 Posts; Posts: 132; Joined: Tue Oct 07, 2008 4:59 pm; Thanked: 4 times

Distance

by vladmire » Sat Oct 18, 2008 11:10 am

I'm having a difficult time setting up my equation to answer this question

During a car trip, Maria stopped to rest after she traveled 1/2 of the total distance to her destination. She stopped again after she traveled 1/4 of the distance remaining between her first stop and her destination, and then she drove the remaining 120 miles to her destination. What was the total distance, in miles, from maria's starting point to her destination

280
320
360
420
480

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Source: Beat The GMAT — Problem Solving | Sat Oct 18, 2008 11:10 am

dmateer25: Community Manager; Posts: 1049; Joined: Sun Apr 06, 2008 5:15 pm; Location: Pittsburgh, PA; Thanked: 113 times; Followed by:27 members; GMAT Score:710

by dmateer25 » Sat Oct 18, 2008 11:25 am

Here is how I set it up:

Let X = Total miles

X/2 = Half of the trip

Then she drove 1/4 of the remaining trip so: 1/4 * x/2 = x/8

So at this point we know she drove X/2 miles. Took a break. Then drove X/8 miles and took a break. The remaining miles are 120 so...

X/2 - X/8 = 120

3X/8 = 120

3X = 960

X=320

You could plug in and work backward on this problem also.

Start with 320 Miles

You drive half of the trip

That means you drove 160.

Then you drive 1/4 of the 160. So you drive 40 miles.

160 - 140 = 120 miles left