Question

I am so lost can someone please help me

Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 80 miles per hour and train B is traveling at 100 miles per hour. Train A passes a station at 11:15am. If train B passes the same station at 11:27a.m., at what time will train B catch up with train A?

Answer 1

At 11:27, when B is at the station, train A will have traveled 12 minutes at 80 mph for a distance of 80(1/60) or 16 miles

So draw a line with B at the station on the left, A 16 miles to the right of B.
Let the distance that A still travels before B catches up be x miles, call that point P

So AP = x, BP = x+16
Time for B to reach P is (x+16)/100
time for A to reach P is x/80

but those times are equal, so
(x+16)/100 = x/80
.
.
x = 64

so time for A to reach P is 64/80 = .8 hrs, or 48 minutes.

so the time when it happens is 11:27 + 0:48 = 1:15 pm