Two trains continuously travel between Washington D. C. and Baltimore which are 120 miles apart. The trains start simultaneously, with train A starting in Washington DC and train B starting in Baltimore, and travel at 30 and 90 mph respectively. If 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?

Step-by-step explanation:

Two train traveling in opposite direction

Distance apart the train is 120miles

Train A

Speed =30mph

Train B

90mph

What is common to the train is the same time, they will meet at the same time

Let assume they meet at distance x from from Washington

Then A has travelled x mile distance

Then, B has travelled 120-x mile distance

Time for train A to get to x,, = time for train B to get 120-x

Time=distance/speed

da/Sa=db/Sb

Let da be distance of train A

And db be distance of train B

Sa be speed of train A

Sb be speed of train B

Then,

da/Sa=db/Sb

x/30=120-x/90

Cross multiply

90x=3600-30x

90x+30x=3600

120x=3600

Then, x=3600/120

x=30miles

Then will meet at 30miles from Washington

Second part of the questions

Train B is faster than train A

Train B has already travelled 90miles while train B travels 30 miles

This shows that train A will not get to Baltimore before train B catch up

Then, let train A travel y distance

Then B will have to complete the 30 miles and then with another 30 miles that A has travel and then y

Total distance B travel will be

db=30+30+y

db=60+y

And da=y

Therefore,

da/Sa=db/Sb

y/30=60+y/60

Cross multiply

60y=1800+30y

60y-30y=1800

30y=1800

Then, y=1800/30

y=60miles

That means they will meet at 60miles from both Washington and Baltimore, or they are at mid points