T-S-Distance

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adthedaddy: Master | Next Rank: 500 Posts; Posts: 167; Joined: Fri Mar 09, 2012 8:35 pmFollowed by: 3 members; Thanked: 39 times

by adthedaddy » Wed Oct 10, 2012 8:14 am

There are 13 equidistant bus stops on a straight road. A bus running at 60 km/hr is some distance
away from the 1st stop from where it will move towards the 13th stop. Two cars start running from
the 6th stop in opposite directions with the same speed. If the bus meets one of the cars at the 1st
stop and the other at the 13th stop, then find the speed of the cars.
(a) 10 km/hr
(b) 20 km/hr
(c) 30 km/hr
(d) 40 km/hr
(e) Cannot be determined

OA:[spoiler] (a)[/spoiler]

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Source: Beat The GMAT — Problem Solving | Wed Oct 10, 2012 8:14 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Oct 10, 2012 9:01 am

adthedaddy wrote:There are 13 equidistant bus stops on a straight road. A bus running at 60 km/hr is some distance
away from the 1st stop from where it will move towards the 13th stop. Two cars start running from
the 6th stop in opposite directions with the same speed. If the bus meets one of the cars at the 1st
stop and the other at the 13th stop, then find the speed of the cars.
(a) 10 km/hr
(b) 20 km/hr
(c) 30 km/hr
(d) 40 km/hr
(e) Cannot be determined

OA:[spoiler] (a)[/spoiler]

Since 6-1 = 5, the distance between the 6th stop and the 1st stop = 5 stops.
The two cars are traveling at the same speed.
Thus, when the 1st car reaches the 1st stop (5 stops to the LEFT of the 6th stop), the 2nd car will reach the 11th stop (5 stops to the RIGHT of the 6th stop).

Let the distance between stops = 10km.

For the bus to catch up to the second car at the 13th stop, the bus must take the same amount of time to travel 120 km (from the 1st stop to the 13th stop) as the 2nd car takes to travel 20 km (from the 11th stop to the 13th stop).
Since the speed of the bus is 60km per hour, the time for the bus to travel 120km = 120/60 = 2 hours.
Speed needed for the car to travel 20km in 2 hours = 20/2 = 10km per hour.

The correct answer is A.

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