If Lucy walks to work at a rate of 4 miles per hour. . . .

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

If Lucy walks to work at a rate of 4 miles per hour. . . .

by Vincen » Sun Oct 08, 2017 11:28 am

If Lucy walks to work at a rate of 4 miles per hour, but she walks home by the same route at a rate of 6 miles per hour, what is Lucy's average walking rate for the round trip?

A. 4.2 miles/hour
B. 4.4 miles/hour
C. 4.8 miles/hour
D. 5 miles/hour
E. 5.8 miles/hour

The OA is C.

How can I determine the solution here?

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Source: Beat The GMAT — Problem Solving | Sun Oct 08, 2017 11:28 am

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Sun Oct 08, 2017 10:05 pm

Vincen wrote:If Lucy walks to work at a rate of 4 miles per hour, but she walks home by the same route at a rate of 6 miles per hour, what is Lucy's average walking rate for the round trip?

A. 4.2 miles/hour
B. 4.4 miles/hour
C. 4.8 miles/hour
D. 5 miles/hour
E. 5.8 miles/hour

The OA is C.

How can I determine the solution here?

The average speed is not equal to the average of 4 and 6. We cannot take an arithmetic average.

Say the distance is 12 miles. I assumed the distance 12 miles since 12 is the LCM of 4 and 6.

Time taken while going to work = 12/4 = 3 hours;
Time taken while coming to home = 12/6 = 2 hours

Average speed = (Total distance) / (Total time) = (12 + 12) / (3 + 2) = 24/5 = 4.8 miles per hour

The correct answer: C

Hope this helps!

-Jay

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

by [email protected] » Mon Oct 09, 2017 2:39 pm

Hi Vincen,

Since this question gives us just the two rates to work with, we can solve it by TESTing VALUES.

The two speeds are 4 miles/hour and 6 miles/hour, so we should choose a common multiple of those two numbers for the one-way distance. Let's TEST 12 miles.

Walking to work:
D = (R)(T)
12mi. = (4 miles/hr)(X hours)
3 hours = X

Walking from work:
D = (R)(T)
12mi. = (6 miles/hr)(Y hours)
2 hours = Y

Total Distance = 12 + 12 = 24 miles
Total Time = 3 + 2 = 5 hours
Average Speed (round-trip) = 24/5 = 4.8 miles/hour

Final Answer: C

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Rich

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8085; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: If Lucy walks to work at a rate of 4 miles per hour. . . .

by Scott@TargetTestPrep » Sat Jan 18, 2020 1:03 pm

Vincen wrote: ↑
Sun Oct 08, 2017 11:28 am
If Lucy walks to work at a rate of 4 miles per hour, but she walks home by the same route at a rate of 6 miles per hour, what is Lucy's average walking rate for the round trip?

A. 4.2 miles/hour
B. 4.4 miles/hour
C. 4.8 miles/hour
D. 5 miles/hour
E. 5.8 miles/hour

The OA is C.

How can I determine the solution here?

We can use the equation:

average speed = (total distance)/(total time)

If we let distance each way = 12, we have:

Average = (12 + 12)/(12/4 + 12/6)

Average = 24/5 = 4.8 mph

Answer: C

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