Question

The train ride from Boston to NYC is 221 miles. Leaving at 7:30 AM at an average rate of 34 mph and stopping for 4 minutes at each of 10 stations, at what time will the train arrive in NYC?

Answer 1

Answer:

Let:

be the distance between cities;

be the rate of Train B.

"An hour later (so at 4:00PM), Train A passes Train B" --> before they pass each other A traveled 1 hour (4PM-3PM) and B traveled 1/6 hours (4PM-3:50PM).

"Combined travel time of the two trains is 2 hours" --> d/100(time to cover all distance for train A)+d/x(time to cover all distance for train B)=2 --> ;

As before they pass A traveled 100 miles (1 hour at 100 miles per hour), then distance to cover for B after they pass is this 100 miles and as B traveled x*1/6 miles before they pass (1/6 hour at x miles per hour), then distance to cover for A after they pass is this x*1/6 miles --> ;

So, we have:

and .

Solving for and

and ;

OR:

and .

(1) Says that train B arrived before A.

If A arrives at 4:20, B at 4:30, not good;

If A arrives at 4:30, B at 4:20, OK.

Sufficient

(2) Says that --> --> , arrival time for B 4:20. Sufficient