I am having trouble with distance calculation (1)

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candygal79: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Mon Feb 10, 2014 1:18 amFollowed by: 3 members

by candygal79 » Wed Mar 19, 2014 8:31 pm

A certain mule travels at 2/3 the speed of a certain horse. If it takes the horse 6 hours to travel 20 miles, how many hours will the trip take the mule ?

4
8
9
10
30

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Source: Beat The GMAT — Problem Solving | Wed Mar 19, 2014 8:31 pm

theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Wed Mar 19, 2014 9:00 pm

Horse = H
Mule = 2/3H

Horse
T = 6hr
D = 20 miles
S = 20/6 = 10/3

Speed of Mule = 2/3 * 10/3 = 20/9

Total Time = 20/(20/9) = 9

R A H U L

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Thu Mar 20, 2014 8:04 pm

Hi candygal79,

This question is ultimately about how a difference in speeds will affect a difference in time. The distance could be ANY distance and the answer will be the same.

To that end, here's a slightly simpler version of this question, using the same data for everything but the distance (which we'll set at 18 miles)

Horse: takes 6 hours to travel 18 miles.

D = R x T
18 = R x 6

Rate = 3mph

Mule: travels 2/3 the speed of the horse = 2/3 of 3 = 2mph

D = R x T
18 = 2 x T

Time = 9 hours

Final Answer: C

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Rich

Contact Rich at [email protected]

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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 » Fri Mar 21, 2014 1:06 am

candygal79 wrote:A certain mule travels at 2/3 the speed of a certain horse. If it takes the horse 6 hours to travel 20 miles, how many hours will the trip take the mule ?

4
8
9
10
30

TIME AND RATE are RECIPROCALS.
Since the mule travels at 2/3 the horse's speed, the mule will require 3/2 the horse's time:
(3/2)(6 hours) = 9 hours.

The correct answer is C.

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