primmadona wrote:

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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