Distance Speed Time - how to solve only by logic?

[Dona]

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 only using 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

[[email protected]]

Hi Dona,

If you're talking about some basic 'brute force' arithmetic, then you can keep track of the relative distances that both Tom and Linda have traveled at specific points in time. Based on the starting times and speeds involved, we know that....

After 1 hour:
Linda = 2 miles
Tom = 0 miles

Since the answer choices are all between 1 hour and 2 hours, inclusive, I'm going to start tracking distances every HALF hour...

After 1.5 hours:
Linda = 3 miles
Tom = 3 miles

At this point, we know that Tom and Linda have traveled the SAME distance.

After 2 hours:
Linda = 4miles
Tom = 6 miles

After 2.5 hours:
Linda = 5 miles
Tom = 9 miles

After 3 hours:
Linda = 6 miles
Tom = 12 miles

At this point, we know that Tom has traveled the TWICE Linda's distance.

We're asked to determine the time (in minutes) that it took Tom to go from Linda's Distance to twice Linda's Distance:
3 hours - 1.5 hours = 1.5 hours = 90 minutes

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

[GMATGuruNY]

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

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

Every 30 minutes, Linda travels 1 more mile, while Tom travels 3 miles (since his rate is 6mph).

Thus, 30 minutes later:
Linda = 2+1 = 3 miles.
Tom = 3 miles.
Same distance traveled by each.

1 hour later:
Linda = 3+1 = 4 miles.
Tom = 3+3 = 6 miles.

1.5 hours later:
Linda = 4+1 = 5 miles.
Tom = 6+3 = 9 miles.

2 hours later:
Linda = 5+1 = 6 miles.
Tom = 9+3 = 12 miles.
Tom has traveled twice the distance that Linda has covered.

2 hours later - 30 minutes later = 90 minutes.

The correct answer is D.