I know this has been asked a couple of times but I REALLY don't understand the second part.

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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?

60
72
84
90
120

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My question is Why do you double Linda's distance instead of just doubling Tom's time? Can you explain why the answers are so different?

Hi,

I am seeing this problem for the first time... So, not sure how usually people solve this problem. However, I would explain how I solved it...

(You cannot double Tom's time as we do not know how much time it took for Tom to travel twice the distance of Linda. We need to figure out that time. All we know is that Tom covered twice as much as Linda. So, you have to write Distance covered by Tom = 2 times the distance covered by Linda. In other words, Dt = 2 * Dl)

We know,
Speed of Tom (say St) = 6 m/hr
Speed of Linda (say Sl) = 2 m/hr

We need to find

1) Amount of time it takes for Tom to cover the exact distance that Linda has covered.


Distance travelled by Tom = Distance travelled by Linda
=> StTt = SlTl

But, Linda had a head start. Hence, she travelled an hour more than Tom. So, Tl = Tt + 1

So, we can rewrite StTt = SlTl as below
StTt = Sl(Tt + 1)

Now substitute speed from the question
StTt = Sl(Tt + 1) => 6Tt = 2(Tt + 1)
=> 3Tt = (Tt + 1)
=> 2Tt = 1
=> Tt = ½ hour or 30 minutes

Now, we have the time takes for Tom to cover the same distance that Linda has covered – 30 minutes.

2) Amount of time it takes Tom to cover twice the distance that Linda has covered.


Distance travelled by Tom = 2 * Distance travelled by Linda
=> StTt = 2*SlTl

But, again, Linda had a head start. Hence, she travelled an hour more than Tom. So, Tl = Tt + 1

So, we can rewrite StTt = SlTl as below
StTt = 2*Sl(Tt + 1)

Now substitute speed from the question
STTT = 2*Sl(Tt + 1) => 6Tt= 2*2(Tt + 1)
=> 6Tt = 4Tt + 4
=> 2Tt = 4
=> Tt = 2 hours or 120 minutes

Now, we have the time takes for Tom to cover twice the distance that Linda has covered – 120 minutes.

All question is asking us to find the difference between 1st and 2nd times.
That is 120 – 30 = 90 mins.

Please see this thread: walk-away-2-tom-linda-stand-at-point-a-t10345.html I think it asks your exact question.

_________________
Jamie Nelson
ManhattanGMAT Instructor