Bunuel wrote:

Train X leaves New York at 1 A.M. and travels east at a speed of x miles per hour. If train Z leaves New York at 2 A.M. and travels east, at what rate of speed will train Z have to travel in order to catch train X at exactly 5:30 A.M.?

(A) 5x/6

(B) 9x/8

(C) 6x/5

(D) 9x/7

(E) 3x/2

This question can be approached with the "close the gap in a chase" method, and by choosing numbers.

Train A, when traveling alone, creates the distance between A and B. That's the gap.

When Train B starts moving, the chase is on.

Time = 3.5 hours

B chases A, closes the gap, only while both move.

B closes the gap at a relative speed, r, of (B's rate - A's rate). What is r? rt = D, so...

The gap will close at D/t = r.

To find r, pick an easy "gap" distance: 70 mi (because t = 3.5)

A travels for 1hr, A's rate = 70 mph = x

The distance/gap of 70 mi is closed by relative speed of (B-A)

Relative speed? D/t = r

70/3.5 = 20

The difference between A's speed and B's speed is 20 mph.

B is chasing; B travels at 20 mph faster than A

B's speed: (70 + 20) = 90 mph

With x = 70, check choices until the answer is 90.

(A) 5x/6 = 350/6 = 5_. No

(B) 9x/8 = 6300/8 = 7_. No

(C) 6x/5 = 4200/5 = 8_. No

(D) 9x/7 = 6300/7= 90. MATCH

(E) 3x/2 = 210/2 = 105. No

Answer D