Train X leaves New York at 1 A.M. and travels east at a speed of x mil

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

let the speed of train X=10m/hr
It has traveled from 1 am till 5.30am, total of 4.5 hrs
Distance=10*4.5=45 miles
This distance has to be covered by train z in 3.5 hrs(it travels from 2 am to 5.30am)
let the speed of z=s
45=sx3.5=450/35=90/7
Now in answer choice plugin value of speed of train X=10
the correct answer is D=90/7

Train X leaves at 1 A.M. and Train Z leaves New York at 2 A.M.
When they meet at 5:30 A.M., Train X's travel time will be 4.5 hours, and Train Z's travel time will be 3.5 hours
Also recognize that, when the trains meet, they both will have traveled the same distance.

We know that Train X travels at x mph, and we want to find Train Z's speed.
So, let z = Train Z's speed (in mph)

Now let's create an equation we can work with!

Let's start with a word equation:
Distance traveled by Train X = Distance traveled by Train Z
distance = (time)(speed)

So, we get: (4.5 hours)(x mph) = (3.5 hours)(y mph)
Simplify: 4.5x = 3.5y
Solve for y to get: = 4.5x/3.5
Check answer choices....not there.
So, take 4.5x/3.5, and multiply top and bottom by 2 to get the EQUIVALENT fraction: 9x/7
Check answer choices....answer: D

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