Speed & distance Problem 1

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.

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