Train A leaves a station traveling 50 MPH. 6 hours later, Train B leaves the same station traveling at 60 MPH?

How long does it take for Train B to catch up to Train A???

after 6 hrs... A has traveled 300miles

300+50t = 60t
10t = 300
t = 30 (after 30 hours).



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After 6 hours train A has travelled 300miles. The difference in speed is 10MPH so to catch up 300miles it will take 30 hours.

For train B to catch up, both will have to travel the same distance. Distance = speed x time.
Suppose it will take train B x hours to travel the distance where it catches up to train A. Therefore, since train A left 6 hours before, it will take train A (x+6) hours to travel the same distance.
Since both distances are equal, we have
50(x+6) = 60x
where 50 is the speed of train A and (x+6) is travel time of train A, while 60 is the speed of train B and x is travel time of train B.
Solving the equation,
50x + 300 = 60x
300 = 10x
30 = x
So it will take train B 30 hours to catch up to train A.

let t be the time it takes train A to catch train B. Since train a leave 6 hrs earlier, t + 6 is the time at which train B catches train A.

when train B catches train A, they are in a same position
A = B

d = rt

A = 50(t+6)
B = 60t

50(t + 6) = 60t
50t + 300 = 60t
10t = 300
t = 30 hrs <== answer