Question

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?

Answer 1

Then 1/2 or 30 minutes is the required time for Tom to cover the exact distance that Linda one hour before.

Two hours after Tom began Tom would cover 12 miles and three hours after Linda started Linda would be 6 miles far away from the starting point

Explanation:

Linda walks in a straight line at 2 miles/hour

then after t ( hours time) she is 2 (m/h) * t = d (L)

for Tom running at 6 m/h starting one hour later to cover the same distance d(L)

d(L) = 6 m/h * ( t - 1 ) then:

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

2*t = 6*t - 6

4*t = 6

t = 6/4

t = 1,5 h

Checking that result.

we see that in 1,5 hours Linda has covered 2* 1,5 = 3 miles

and in 0.5 hours Tom covered the same distance 0,5 * 6 = 3 miles

NOTE: Remember that tom started one hour later.

Then 1/2 or 30 minutes is the required time for Tom to cover the exact distance that Linda one hour before.

b) In this case

d(T) = 6* ( t - 1 ) must be equal to twice of the Linda distance

d(L) = 2 * 2 * t

6*t - 6 = 4*t

2*t = 6

t = 3

To check it

in 3 hours Linda had covered 3 * 2 = 6 miles

in 2 hours Tom had covered 2 * 6 = 12 miles