mohnish104 wrote:
Train A left station T at 3:30 p.m. and traveled on straight tracks at a constant speed of 60 miles per hour. Train B left station T on adjacent straight tracks in the same direction that train A traveled on. Train B left station T 40 minutes after train A, and traveled at a constant speed of 75 miles per hour. Train B overtook train A on these straight tracks. At what time did train B overtake train A?
4:10
5:40
6:10
6:50
7:30
Dear mohnish104,
I'm happy to help you with this.
First of all, here's a blog you may find helpful:
http://magoosh.com/gmat/2012/gmat-dista ... e-formula/To start, we need to know how far away Train A was at the moment B started. Train B started at 4:10 pm, 40 minutes after A. Train A moves at 60 mph, which is equivalent to a mile per minute, so in 40 minutes, A has traveled 40 miles. That's how far A is.
Now, B will gain on A at the rate of their difference in speeds --- 75 mph - 60 mph = 15 mph. That's the rate at which the gap between two trains closes. Furthermore, 15 mph is a rate of 1 mile every 4 minutes, for B to close an initial gap of 40 miles will take 40*4 = 160 minutes. That time, 160 minutes is 2 hours and 40 minutes, so this amount of time after 4:10 pm, namely at 6:50 pm, is when the gap has shrunk to zero and B passes A.
Does this make sense?
Mike
_________________
Mike McGarry
Magoosh Test PrepEducation is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)