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 the exact 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)120

OAD

Guys ,

Let Distance be D , speed be S , and Time be T.

Linda's S = 2 m/h
Linda's T = 1 h (60 min)

So Linda's D will be = 2 X 1 = 2

Now given that Tom's S = 6 m/h

So Tom's T to cover 2 mile will be = 2/6*60 = 20 min

If Tom is taking 20 min to cover 2 miles than for 4 miles it will be 40 min and Linda will take to cover 4 miles is 120 min.

Now what next......

Pls suggest me and correct me if i am wrong.

Linda's speed = 2 mil/hr
Hence Linda travels 1 Mile in 30 Mins
Tom's Speed = 6 mil/hr
Hence Tom travels 1 Mile in 10 Mins.

As Linda has a head start of an hour she has already covered 2 miles.

At 1 hr 30 mins -> Linda = 3 mil and Tom = 3 mil
At 2 hr -> Linda = 4 mil and Tom = 6 mil
At 2 hr 30 mins -> Linda = 5 mil and Tom = 9 mil
At 3 hr -> Linda = 6 mil and Tom = 12 mil

Hence Distance is same at the 1 hr 30 mins mark = 90 mins
Tom's distance is twice as that of Linda at 3 hour mark - 180 mins

Difference = 180 - 90 = 90

Ans : D

j_shreyans 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 the exact 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)120

After 1 hour of walking at 2 miles per hour, Linda has traveled r*t = 2*1 = 2 miles.

Every 30 minutes, Linda travels 1 more mile, while Tom travels 3 miles (since his rate is 6mph).

Thus, 30 minutes later:
Linda = 2+1 = 3 miles.
Tom = 3 miles.
Same distance traveled by each.

1 hour later:
Linda = 3+1 = 4 miles.
Tom = 3+3 = 6 miles.

1.5 hours later:
Linda = 4+1 = 5 miles.
Tom = 6+3 = 9 miles.

2 hours later:
Linda = 5+1 = 6 miles.
Tom = 9+3 = 12 miles.
Tom has traveled twice the distance that Linda has covered.

2 hours later - 30 minutes later = 90 minutes.

The correct answer is D.

I like your algebraic approach: here's how I'd fix it.

Linda's rate = 2 mph
Linda's time = t hours

Tom's rate = 6 mph
Tom's time = (t - 1) hours (since Linda has a one hour headstart).

When they travel the SAME distance, 2t = 6*(t-1). This reduces to t = 3/2.

Now we need Tom to double up Linda. This is the same equation as before, except we DOUBLE Linda's distance. This gives us 2*(2t) = 6*(t-1), or t = 3.

The difference between the times is 3 - (3/2), or (3/2) of an hour. (3/2) of an hour = 90 minutes, and we're done.