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Tom and Linda stand at point A. Linda begins to walk in a straight

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Joined: 13 Sep 2016
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Tom and Linda stand at point A. Linda begins to walk in a straight  [#permalink]

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Updated on: 09 Jul 2017, 21:36
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Difficulty:

55% (hard)

Question Stats:

67% (02:42) correct 33% (02:57) wrong based on 56 sessions

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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 the exact 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. 120

Hi All,
I found this word question on distance- speed- time which I was able to solve quickly by using algebra, but somehow I cannot solve it by using only logic and arithmetic. I will really appreciate if you can help with detailed approach of how to solve this problem using only logic and arithmetic (not algebra)

Thank you,
Dona

Originally posted by primmadona on 09 Jul 2017, 11:19.
Last edited by Bunuel on 09 Jul 2017, 21:36, edited 1 time in total.
Renamed the topic, edited the question and moved to PS forum.
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Re: Tom and Linda stand at point A. Linda begins to walk in a straight  [#permalink]

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09 Jul 2017, 14:38
Hi All,
I found this word question on distance- speed- time which I was able to solve quickly by using algebra, but somehow I cannot solve it by using only logic and arithmetic. I will really appreciate if you can help with detailed approach of how to solve this problem using only logic and arithmetic (not algebra)

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 the exact distance that Linda has covered and the amount of time it takes Tom to cover twice the distance that Linda has covered?
60
72
84
90
120

Thank you,
Dona

Nice question. It's always worth trying to figure out a simpler way of approaching a problem.

I typically do these by creating a chart. One column of the chart is 'time'. The other columns tell me where each person in the problem is located at that time.

In this problem, it would look like this. I started counting up in 12-minute intervals, because all of the answer choices are multiples of 12. 12 minutes is 0.2 hours. In 0.2 hours, Tom will travel 1.2 miles and Linda will travel 0.4 miles.

0 hours:
Tom: 0, Linda: 0

1 hour:
Tom: 0, Linda: 2

1.2 hours:
Tom: 1.2
Linda: 2 + 0.4 = 2.4

1.4 hours:
Tom: 1.2 + 1.2 = 2.4
Linda: 2.4 + 0.4 = 2.8

1.6 hours:
Tom: 2.4 + 1.2 = 3.6
Linda: 2.8 + 0.4 = 3.2

1.8 hours:
Tom: 3.6 + 1.2 = 4.8
Linda: 3.2 + 0.4 = 3.6

2.0 hours:
Tom: 4.8 + 1.2 = 6.0
Linda: 3.6 + 0.4 = 4.0

2.2 hours:
Tom: 6.0 + 1.2 = 7.2
Linda: 4.0 + 0.4 = 4.4

2.4 hours:
Tom: 7.2 + 1.2 = 8.4
Linda: 4.4 + 0.4 = 4.8

2.6 hours:
Tom: 8.4 + 1.2 = 9.6
Linda: 4.8 + 0.4 = 5.2

2.8 hours:
Tom: 9.6 + 1.2 = 10.8
Linda: 5.2 + 0.4 = 5.6

3.0 hours:
Tom: 10.8 + 1.2 = 12.0
Linda: 5.6 + 0.4 = 6.0

Unfortunately this didn't give us an exact answer, but it's close enough that we can estimate. Tom and Linda covered the same distance at about 1.5 hours. Tom covered twice Linda's distance in exactly 3 hours. The difference is 3-1.5 = 1.5 hours, which is 90 minutes.
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Tom and Linda stand at point A. Linda begins to walk in a straight  [#permalink]

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Updated on: 21 Jul 2017, 03:28
2
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 the exact 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. 120

Hi All,
I found this word question on distance- speed- time which I was able to solve quickly by using algebra, but somehow I cannot solve it by using only logic and arithmetic. I will really appreciate if you can help with detailed approach of how to solve this problem using only logic and arithmetic (not algebra)

Thank you,
Dona

Here is the logical way to solve this..

Speed of Tom = 6 mph
Speed of Linda = 2 mph

Relative speed of Tom = 6-2 = 4 mph.

So Compared with Linda, Tom will cover 4 additional miles per hour.

Linda has a head start of 1 hour in which she has covered 2 miles.

Time taken by Tom to cover the same distance as Linda =$$\frac{(Lead Taken by Linda)}{(Relative Speed of Tom} = \frac{2}{4} = \frac{1}{2} = 30 Minutes$$

So, 30 Minutes after Tom started, he will have traveled the same distance as that by Linda, which is 3 miles.

Now, Following are the distances covered by Tom and Linda Henceforth.. (Back Solving..)

1 hour after they have traveled the same distance..

Distance by Tom = 3 + 6 = 9 miles
Distance by Linda = 3 + 2 = 5 miles.

Option A is out.
120 minutes is too large. E is out.

Lets Put in C as it will help us solve the question fastest now.

After 1 hour, distances stand at

Distance by Tom = 3 + 6 = 9 miles
Distance by Linda = 3 + 2 = 5 miles.

So, after 84 minutes = 60 + 24 minutes,

Distance by Tom = 9 + 2.4 = 11.4 miles
Distance by Linda = 5 + 0.8 = 5.8 miles.

5.8 * 2 = 11.6 - 11.4 = 0.2

C is out and since Tom hasn't covered twice the distance so far, D is answer.

Edit: Fixed the grammar

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Originally posted by umg on 10 Jul 2017, 02:55.
Last edited by umg on 21 Jul 2017, 03:28, edited 1 time in total.
Intern
Joined: 24 Jun 2017
Posts: 14
Re: Tom and Linda stand at point A. Linda begins to walk in a straight  [#permalink]

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10 Jul 2017, 06:26
1
1
1.
2+2x=6x
X=0.5
60(0.5+1)=90
2.
6x=2(2+2x)
X=2
60(2+1)=180
3.
180-90=90
I am wondering why you use such a complex method
Re: Tom and Linda stand at point A. Linda begins to walk in a straight   [#permalink] 10 Jul 2017, 06:26
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