Problem Solving

Q. 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 of 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

Unfortunately, I don't have/know the solution to the above problem. Please advise.

Thanks,
M

Suppose D = TS where D=distance, T=Time and S=Speed
To travel half distance, (2+2T) = 6T ==> T = 1/5 ==> 12 minutes
To travel double distance, 2(2+2T) = 6T ==> 2 ==> 120 minutes
Difference, 108 minutes

E is the answer...

MI3 wrote:Q. 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

Unfortunately, I don't have/know the solution to the above problem. Please advise.

Thanks,
M

Many tricky problems can be solved quickly and efficiently with a little trial and error.

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.

IMO E is Correct

GMATGuruNY wrote:

MI3 wrote:Q. 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

Unfortunately, I don't have/know the solution to the above problem. Please advise.

Thanks,
M

Many tricky problems can be solved quickly and efficiently with a little trial and error.

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.

hello mitch

could you please explain a bit further how do we find 15 mins or in other words on what basis do we take 15 mins??

regards nafi

thanks in advance

(t-1) * 6 = 2*t/2

=> 6t - 6 = t

=> t = 6/5

(T-1) * 6 = 2* T * 2

=> 6T - 6 = 4T

=> T = 6/2

So T - t * 60 = 6 * 60 * (0.5 - 0.2)

= 36 * 3 = 108 min

Answer - E

nafiul9090 wrote:

GMATGuruNY wrote:

MI3 wrote:Q. 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

Unfortunately, I don't have/know the solution to the above problem. Please advise.

Thanks,
M

Many tricky problems can be solved quickly and efficiently with a little trial and error.

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.

hello mitch

could you please explain a bit further how do we find 15 mins or in other words on what basis do we take 15 mins??

regards nafi

thanks in advance

I started with 15 minutes because of the difference between the two rates.
In 1 hour, Tom travels travels 6 miles, while Linda travels only 2 miles.
Thus, the time that it will take Tom to travel 1/2 the distance that Linda has traveled -- even with the 1 hour head start given to Linda -- must be quite short.

subhashghosh wrote:(t-1) * 6 = 2*t/2

=> 6t - 6 = t

=> t = 6/5

(T-1) * 6 = 2* T * 2

=> 6T - 6 = 4T

=> T = 6/2

So T - t * 60 = 6 * 60 * (0.5 - 0.2)

= 36 * 3 = 108 min

Answer - E

Doing calculations by conventional methods, in some cases, can be less confusing , and this is a perfect example !!

1. Time to cover 1/2 distance covered by Linda.

Let Linda travels X miles. Therefore time required to travel X miles = T1 = X/2 Hrs

Tom need to travel 2+X/2 miles. Time required by mike to travel 2+x/2 miles = T2 = 2+x/12 Hrs

As T1 = T2
X/2 = 2+x/12 ... therefore X=2/5 miles. which leads T2 = 2+x/12 = 12 mins.

2. Time to cover double the distance covered by Linds
Let Linda travels Y miles
Time taken by Linda = Y/2 Hrs
Time taken by Mike to cover double the distance = (2+Y)2/6 = 4 + 2Y/6
Now Y/2 = (4+2Y)/6 .. Therefore Y = 4
Time taken by mike to cover 12 Miles = 12/6 = 2 Hrs = 120 Mins

Difference between 1 and 2 = 120 -12 mins. = 108 mins.
Answer = E

Nice explanation gmatguruny...

Linda: Rate=2, Time=x+1, D= 2x+2
Tom: Rate=6, Time=x, D= 6x

6x=2x+2 => x=.5 Plug in, 3=3 => Tom will cover the same distance as Linda after he jogs for 30 minutes, so he can cover half that in 15 minutes.

Then I created a table assuming Tom travels 3 miles in 30 minutes while Linda travels 1 mile in that time:

T : L
6 : 4 (60 minutes)
9 : 5 (90 minutes)
12: 6 (120 minutes)

So Tom's distance is double Linda's in 120 minutes.

120-15= 105. E.