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shanice: Master | Next Rank: 500 Posts; Posts: 110; Joined: Thu Apr 05, 2012 8:48 amFollowed by: 1 member; Thanked: 3 times

by shanice » Thu Aug 23, 2012 2:00 am

Stacy and Heather are 20 miles apart and walk towards each other along the same route. Stacy walks at a constant rate that is 1 mile per hour faster than Heather's constant rate of 5 miles/hour. If Heather starts her journey 24 minutes after Stacy, how far from her original destination has Heather walked when the two meet?

A)7 miles
B)8 miles
C)9 miles
D)10 miles
E)12 miles

I get to solve only some part of this question. I know that Stacy covered 2.4 miles in 24 minutes.

I need someone to explain the logic in this sentence "Since both are walking towards each other, the sum of their speeds are 6+5=11 miles/hr.

Thank you

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Source: Beat The GMAT — Problem Solving | Thu Aug 23, 2012 2:00 am

mssharsha: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Thu Aug 23, 2012 2:34 am; Thanked: 1 times

by mssharsha » Thu Aug 23, 2012 2:57 am

Stacy has covered 2.4 miles in 24 minutes. Now the distance that has to be covered by both Stacy and Heather together is 17.6 miles. In 60 min they'll travel (6+5)=11 km.. in 90 min (9+7.5)=16.5 in 91 min (9+0.6 + 7.5+0.5)=17.6.. So the distance as asked travelled by Heather is 8 miles..

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niketdoshi123: Master | Next Rank: 500 Posts; Posts: 210; Joined: Thu Mar 08, 2012 11:24 pmFollowed by: 3 members; Thanked: 62 times

by niketdoshi123 » Thu Aug 23, 2012 3:42 am

shanice wrote:
I need someone to explain the logic in this sentence "Since both are walking towards each other, the sum of their speeds are 6+5=11 miles/hr.

Thank you

This question tests the concept of relative speed.

When two people/objects travel in opposite direction, either towards each other or away from each other, their relative speed with respect to each other is the sum of the their individual speed.

and when two people/objects travel in the same direction their relative speed will be the difference between the two speeds.

Since in this question Stacy and Heather are walking towards each other , their relative speed will be the sum of the their speeds. Hence 6+5 = 11 miles/hr

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shanice: Master | Next Rank: 500 Posts; Posts: 110; Joined: Thu Apr 05, 2012 8:48 amFollowed by: 1 member; Thanked: 3 times

by shanice » Thu Aug 23, 2012 6:22 am

Got it, guys.

Thank you very much.

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