Problem Solving

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

Would say E

Distance covered by Linda in a min = 1/30
Distance covered by Tom in a min = 1/10

In 120 mins tom would be exactly 2 times the distance covered by Linda.
while he starts an hour later by that time Linda would have covered 2miles now it takes 12 minutes for Tom to reach 1.2 miles which is exactly 1/2 the distance covered by linda in the same time.
hence 120-12 = 108 is correct choice...

We know Linda has already traveled 2 miles before things really get going:

(2+2t)(1/2) = 6t
1+t = 6t
t =1/5 = 12 min

(2+2t)(2) = 6t
4+4t = 6t
2t = 4
t =2 or 120 minutes

120 min - 12 min = 108 min.

E

anksbhandari 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 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

Hi understood the 120 minutes .. but can someone explain me the 12 mints ?

egybs wrote:We know Linda has already traveled 2 miles before things really get going:

(2+2t)(1/2) = 6t
1+t = 6t
t =1/5 = 12 min

(2+2t)(2) = 6t
4+4t = 6t
2t = 4
t =2 or 120 minutes

120 min - 12 min = 108 min.

E

anksbhandari 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 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

@ sudhir3127: If you understood the set up of equations that egybs used, especially for that which resulted in 120 minutes, how do you have trouble understanding the set up which resulted in 12 minutes?
They are the same logic.

(2+2t)(1/2) = 6t <---Here (1/2)Distance of Linda = Distance of Tom
1+t = 6t
t =1/5 = 12 min <--- Here, Time(of Tom) = 1/5 hr*(60 min/hr) = 12 min