Speed and Distance

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winnerhere: Master | Next Rank: 500 Posts; Posts: 231; Joined: Thu Apr 12, 2007 2:45 am; Thanked: 5 times; Followed by:1 members

Speed and Distance

by winnerhere » Thu Aug 12, 2010 7:01 pm

Jack and Jill started from A and B , towards B and A , at 6 AM and 7 AM respectively.They met each other at 9AM and continued towards their respective destination.Jack , reaching B turns back and catches up with Jill at 11 AM, before Jill reaches A. At what time Jill reaches A.

1. 7 pm

2) 4 pm

3) 5 pm

4) 6 pm

5) 10 pm

Quote

Source: Beat The GMAT — Problem Solving | Thu Aug 12, 2010 7:01 pm

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pm; Location: Milpitas, CA; Thanked: 447 times; Followed by:88 members

by Rahul@gurome » Thu Aug 12, 2010 8:15 pm

Solution:
Let the distance between A and B be d.
Let Jack's speed be x km/hr and Jill's speed be y km/hr.
Jack starts 1 hour earlier that is at 6AM.

In 1 hour he travels 1*x km or x km.
So distance between them at 7AM is d-x km.
At this time Jill is starting from B.
So when they meet let us say at point p, the time taken is (d - x)/(x+y) which is 9 - 7 or 2 hours.
Or (d-x)/(x+y) =2.
Or d = 3x+2y.
Now after they meet Jack is going on and reaching B.
Also the distance from point P to B is the distance Jill travels in 2 hours which is 2y.
So Jack covers this distance in 2y/x hours.
In this 2y/x hours distance traveled by Jill in the direction of A is y*2y/x = 2y^2/x.

So now after Jack reaches B distance between Jack and Jill is 2y + 2y^2/x. which is 2y(1+y/x).

So time in which Jack catches up with Jill when both are traveling in the direction of A is
{2y(1+y/x)}/(x-y).

Time at which this happens is 11AM.

They are meeting for the first time at 9AM. After this both Jack and Jill are traveling for 2y/x hours before Jack reaches B and after that they are meeting after {2y(1+y/x)}/(x-y) hours.

Or 2y/x + {2y*(1+y/x)}/(x-y) = 11- 9 = 2.

On solving we get x = 3y.

Or d is 9y + 2y is 11y.

Time taken by Jill to cover d is 11y/y is 11 hours.
This is after 7AM .
So Jill reaches A at 6PM.

Rahul Lakhani
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