trains

[ritula]

Two trains continuously travel between Washington DC and Baltimore, which is 120 miles away. They start simultaneously, train A at Washington and train B at Baltimore, and run at 30 and 90 mph respectively. The station turnaround times are negligible. What is the distance between the point where the trains meet for the first time and the point where they meet for the second time?

0
30 miles
60 miles
90 miles
120 miles

[parallel_chase]

Two trains continuously travel between Washington DC and Baltimore, which is 120 miles away. They start simultaneously, train A at Washington and train B at Baltimore, and run at 30 and 90 mph respectively. The station turnaround times are negligible. What is the distance between the point where the trains meet for the first time and the point where they meet for the second time?

0
30 miles
60 miles
90 miles
120 miles

A's rate = 30mph
B's rate = 90 mph

A and B are traveling in opposite direction, therefore,
increasing or decreasing rate is 120mph

total distance = 120 miles

120/120 = 1 hr

Therefore the trains will meet every 1 hr.

first meeting = 30*1 = 30 miles
second meeting = B would still have to cover remaining 30 miles to Washington and start back to Baltimore. Therefore, second meeting will be at 60 miles

difference between the distance's of first meeting and second meeting
60-30 = 30 miles

Hence B

[cramya]

I agree with Parallel chase on the answers which is 30

For the second meeeting:

Train A would still be making its first trip from Washington to Baltimore whereas Train B would have finsihed its first trip from Baltimore to Washington and woulld be travelling towards Baltimore(since its travels 90 mph compared to 30 mph of A's).



Not needed for the problem but explaining if this continues a third time:

If this went around the third time (3rd hour) Train A would still be making its first trip to Baltimore and would have travelled 90 miles but Train B would have finsihed its second trip from Washington to Baltimore and then in its thrid trip of Baltimore to Washington covered 30 miles (The would meet at the 90th mile)

Once you draw a picture of the trips it would make it a whole lot easier to understand this

WASHINGTON BALTIMORE
A B

[cramya]

The key to problems like these are understanding that the 2 objects are converging at the sum of their speeds

30+90 = 120 miles/hr

Therefore the time after which they meet = total distance/combined converging speed

= 120/120 = 1 hr

[ritula]

Yes Ans is 30 indeed.
Thanks 2 all.

[stop@800]

At times trains are traveling in same direction also so I think we can not generalize the rate as 120.

I found answer just by drawing the picture.