Speed & distance Problem 1

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aditiniyer: Senior | Next Rank: 100 Posts; Posts: 45; Joined: Fri Aug 19, 2016 1:42 am

by aditiniyer » Thu Jan 26, 2017 12:03 am

Tom & Linda stand at a point A. Linda begins to walk in a straight line away from Tom at a constant rate of 2 miles/hr. One hour later, Tom begins to jog in a straight line in the exact opposite direction at a constant rate of 6 miles per hour. If both Tom & Linda travel indefinitely, what is the positive difference in minutes between the amount of time it takes Tom to cover half the distance that Linda has covered and the amount of time it takes Tom to cover twice the distance that Linda has covered ?

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Source: Beat The GMAT — Problem Solving | Thu Jan 26, 2017 12:03 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 » Thu Jan 26, 2017 3:11 am

Tom and Linda stand at point A. Linda begins to walk in a straight line away from Tom at a constant rate of 2 miles per hour. One hour later, Tom begins to jog in a straight line in the exact opposite direction at a constant rate of 6 miles per hour. If both Tom and Linda travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes Tom to cover half the distance that Linda has covered and the amount of time it takes Tom to cover twice the distance that Linda has covered?
A. 60
B. 72
C. 84
D. 90
E. 108

After 1 hour of walking at 2 miles per hour, Linda will have traveled r*t = 2*1 = 2 miles.

At this point Tom starts to jog at 6 miles per hour. Since Tom is traveling 3 times as fast as Linda, it won't take long for him to cover half the distance traveled by Linda.

15 minutes later, Tom will have traveled r*t = 6*(.25) = 1.5 miles.
Linda will have traveled a total of 2 + 2*(.25) = 2.5 miles.
Since Tom's distance is a little more than 1/2 of Linda's distance, the time needed for Tom to travel 1/2 of Linda's distance is a little less than 15 minutes.

Since Tom is traveling 3 times as fast, he will need only a few hours to cover twice the distance traveled by Linda.

After 2 hours have passed from when Tom starts to jog:
Tom will have traveled r*t = 6*2 = 12 miles.
Having started 1 hour earlier, Linda will have traveled r*t = 2*3 = 6 miles.
Since 12 = 2*6, the time needed for Tom to travel twice the distance traveled by Linda is 2 hours = 120 minutes.

Since 120-15 = 105 minutes, and Tom needs a little less than 15 minutes to travel 1/2 the distance covered by Linda, the correct answer must be a little more than 105.

The correct answer is E.

Last edited by GMATGuruNY on Thu Jan 26, 2017 4:16 am, edited 1 time in total.

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

by Jay@ManhattanReview » Thu Jan 26, 2017 4:10 am

aditiniyer wrote:Tom & Linda stand at a point A. Linda begins to walk in a straight line away from Tom at a constant rate of 2 miles/hr. One hour later, Tom begins to jog in a straight line in the exact opposite direction at a constant rate of 6 miles per hour. If both Tom & Linda travel indefinitely, what is the positive difference in minutes between the amount of time it takes Tom to cover half the distance that Linda has covered and the amount of time it takes Tom to cover twice the distance that Linda has covered ?

Pl. post the complete question.

Coming to the question.

We are given that Linda's speed = 2 mph, thus in one hour, Linda is 2 miles away from point A.

Say Linda walked d miles, thus in the first instance, Tom also travelled d/2 miles and in the second instance, Tom walked 2d miles.

1. The first instance: Tom to cover half the distance that Linda has covered

Time taken by Tom = Time taken by Linda

(d/2)/6 = (d-2)/2 [Linda already has a lead of 2 miles]

=> d/12 = (d-2)/2

=> d = 12/5 miles

=> Tom walked d/2 = 6/5 miles, taking (6/5)/6 = 1/5 hr = 60/5 = 12 minutes

2. The second instance: Tom to cover twice the distance that Linda has covered

Time taken by Tom = Time taken by Linda

(2d)/6 = (d-2)/2 [Linda already has a lead of 2 miles]

=> d/3 = (d-2)/2

=> d = 6 miles

=> Tom walked 2d = 12 miles, taking 12/6 = 2 hr = 120 minutes

Difference of time = |12-120| = 108 minutes.

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Mon Jan 30, 2017 4:51 pm

Tom and Linda stand at point A. Linda begins to walk in a straight line away from Tom at a constant rate of 2 miles per hour. One hour later, Tom begins to jog in a straight line in the exact opposite direction at a constant rate of 6 miles per hour. If both Tom and Linda travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes Tom to cover half the distance that Linda has covered and the amount of time it takes Tom to cover twice the distance that Linda has covered?
A. 60
B. 72
C. 84
D. 90
E. 108

We are given that Linda has a rate of 2 mph and that Tom has a rate of 6 mph. We are also given that Linda begins to walk away from Tom and then one hour later, Tom begins to jog in a straight line in the exact opposite direction. Thus, we can let Linda's time = T + 1, and Tom's time = T.

Let's first determine the number of hours it takes Tom to cover half the distance Linda has gone. Since distance = rate x time, Linda's distance = 2(T + 1) = 2T + 2, and Tom's distance = 6T. So we can create the following equation and determine T:

(1/2)(2T + 2) = 6T

T + 1 = 6T

1 = 5T

T = 1/5 hour = 12 minutes

Next let's determine the number hours it takes Tom to cover twice Linda's distance.

(2)(2T + 2) = 6T

4T + 4 = 6T

4 = 2T

T = 2 hours = 120 minutes.

Thus, the difference in time is 120 - 12 = 108 minutes.

Answer: E

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